{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maximum Likelihood vs Maximum A-posteriori\n",
    "\n",
    "In this notebook, we compare estimating the weights ${\\bf w}$ of a linear regression via ML and MAP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.random import seed\n",
    "from numpy.linalg import inv\n",
    "\n",
    "%config InlineBackend.figure_format = \"retina\"\n",
    "plt.rcParams[\"figure.figsize\"] = (8, 4)\n",
    "plt.rcParams[\"axes.spines.right\"] = False\n",
    "plt.rcParams[\"axes.spines.top\"] = False\n",
    "np.set_printoptions(precision=5, suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating the synthetic data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f8fd7fb7eb0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 474
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "seed(31415)\n",
    "N, M = 11, 11\n",
    "α = 1.3\n",
    "x = np.linspace(0, 1, N) + np.random.rand(N) * 0.05\n",
    "t = 3 * x + 2.3 * x ** 2 + 1.2 + np.random.randn(N) / α\n",
    "Phi = np.stack([x ** m for m in range(M)], axis=-1)\n",
    "\n",
    "plt.scatter(x, t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ML vs MAP for $N=M$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.69066],\n",
       "       [1.3315 ],\n",
       "       [0.94343],\n",
       "       [0.73423],\n",
       "       [0.58872],\n",
       "       [0.47213],\n",
       "       [0.37393],\n",
       "       [0.28953],\n",
       "       [0.21596],\n",
       "       [0.15095],\n",
       "       [0.09268]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_map = inv(α * np.eye(M) + Phi.T @ Phi) @ Phi.T @ t[:, None]\n",
    "w_map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[      16.07303],\n",
       "       [    -748.87085],\n",
       "       [   11337.69034],\n",
       "       [  -79608.42287],\n",
       "       [  313855.55583],\n",
       "       [ -754568.3565 ],\n",
       "       [ 1135820.7735 ],\n",
       "       [-1053174.27092],\n",
       "       [  561534.8151 ],\n",
       "       [ -143877.14885],\n",
       "       [    9425.03585]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_ml = inv(Phi.T @ Phi) @ Phi.T @ t[:, None]\n",
    "w_ml"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pjOlH8MuDTQ0G2eobUu6I92iXsdZWWWv/Rfgo17OP4Pw9uIHF6hLY6YGa8zpt/h0JTJ00LrC6oYVBtkREIo6SYhER720PKTfs1hLaR6+rmxd3hNC+ns1OqxNoWv6d5vaH6MjX432CycB5xphmp34xxswj+IXFe20YrbmzvQwUBMpXtVQ72IJnAo+xwLebOyjws6mbQ9oCz7bjXp3tbGNMSzXmNxLsA7ygwb62vkenAee3L7xOtz2kfERd4wLzh4e2PAg9P/S1+pYxpqVBr75P8HPlMy0cJyIScZQUi4h0EmPMXGPMTcaYZkdcNsaMIlgDU0rjmqrQKV2mdXCInS5QI1c3au1xxphG01sZY1KBp4DBbbhkh70egf6Rdc3XY4GnjDGNRlY2xkzGjZxd566juW9HsNaWhcQRD/yvpcTYGDPVGNOw6e+fCA4G9QNjzKVNnJcIPIIb+RjgGWttW0Yh7mqxwBNN1XgbYy7AjSoNLgG+t8EhK0LK1xtjhjfYjzFmNC7R69LPTcaY/saY3zYVU8gxybja3jofh+z7nDHmiw1qfxuefwJuIC+Ardba+r7AgambXg6sjgD+FegS0fAa1wDfCKyWEJzXWkQkKmigLRGRVhhjLj6Cw18MmRqlP/BH4NfGmLdw87duxX0wz8ENcjOfYI3nH5uYezR0/tVfBz70bwRqAtv2WGvXHEF8XvgTcE+g/LQx5lHcdFQluEHGvoBLuv6Nm8e4JQtxtX4ADxhj/oBrBlw3L/AWa21bpuep8zvgAtygRccA64wx/8SNkB2La4p6LW60X4C/W2tfPILrd6bf4uK+ENfX9SNjzLPAIuAAbm7asbimz8fhRiCuazKNtXZ7YLqe+3DP9WljzPPAS7hRjkfj+quOCJyyh2DiE2mew42mvM4Y83dgDW7wrbnA5QS7HvzQWrsr9ERr7R5jzAJgHm5k+I+NMX8DVhMchOrzuKmB2vIe7UgJwP8B/2eMWY5rNr8e9/PJwP18rwIGBo5/F/e7VWc0bhTtPxljXgeWA7twfZD74Pr7X0ywFv2XTcTwFdzvQ2/caPHTjDEP4aa46oV7/50XcvzXrLX7Gl5ERCSSKSkWEWndkTQXzSQ4bUpd/9d43Ifz5vojWlzS+NNGO6xdbYx5HPgsru9jw4FwHsIllZHsz8BM4HO4JOOawBLqeeAGWk84XsR96D8JN3DSXxrs/3+40a7bJDCX9DnA47imsZm4JKTRoYF73dTWa3c2a601xlyG++LlBlxic1lgaUqjaXCstX8L9M3+Ay7puyiwNLQWuCACmo03526CSfuPmthvgZ9Za//czPlfwSWQk3BTCX2vwX4/bjqm9+japNiGlI8PLM15C7jcWht6Tt3PPAWX/F7czLnVwG3W2gcaBWDtbmPMScB/cUn4GNx0cg2V4xLi7jiCvoh0c0qKRUQ6z8PAKmAObvqTCbja40RcU+ltuA/Z/7TWftTCda4B3gGuwNWs9iKK/n4HPqRfbYx5EfgyrqlmMq42cxXwsLX2SYDWxs4KJLFn4pLTi3AD+6RzFPMaW2tLgQuMMXNxCc9s3BcQtbhEaxFwfyujEnsi0CrhG8aYe4HrcQNODcYldiW45vjvA09Za99t5hr3BX4238B9cTMM9/PJBz7CNW1/2Fpb29T5kcJa+01jzEu4Lwim41pj5OFqT++21n7Qwrn5gWbEN+Jab4wN7NqH+937m7V2qTHmtM57Bk3GtcMYMwT3N+R03O/OENzUR4dx788VwGOBOdEb+gVuzuXP4KaBG4d7b8fh3h+bccn0P1pqYWGt3RRonn8t7kuXKbhB9Or+jr0C/MVaG4kjk4uItMqEf6EoIiIiEvmMMbcTbF1xeoP5dUVERNpMA22JiIiIiIhIj6WkWERERERERHosJcUiIiIiIiLSYykpFhERERERkR5LSbGIiIiIiIj0WBp9WkRERERERHos1RSLiIiIiIhIj6WkWERERERERHosJcUiIiIiIiLSYykpFhERERERkR6rRyTFxphHjTGPeh2HiIiIiIiIRJZYrwPoIuOmTZs2DbjK60BERERERESkU5j2nNQjaopFREREREREmqKkWERERERERHosJcUiIiIiIiLSYykpFhERERERkR5LSbGIiIiIiIj0WEqKRUREREREpMdSUiwiIiIiIiI9lpJiERERERER6bGUFIuIiIiIiEiPpaRYREREREREeiwlxSIiIiIiItJjxXodQKSrrKykuLiYkpISqqursdZ6HZJECWMMcXFxpKWlkZ6eTmJiotchiYiIiIhIA0qKW1BaWsru3buVCEu7WGupqqoiPz+fgoICBg0aRGpqqtdhiYiIiIhICCXFzaisrKxPiNPT08nMzCQxMRGfTy3OpW38fj+VlZUUFhZSXFzM7t27GT58OAkJCV6HJiIiIiIiAUqKm1FcXFyfEA8YMABjjNchSZTx+XwkJyeTlJQEuPfUoUOH6NOnj8eRiYiIiIhIHVV7NqOkpASAzMxMJcRyVIwxZGZmAsH3lYiIiIiIRAYlxc2orq4G0OBI0iHq3kd17ysREREREYkMaj7djLrBtdSHWDpCXWsDDdomIiIiIs3auwo2vgw734c9H0FSJoyaA6PPgtFnQkyc1xF2S0qKRbqAmuCLiIiISLOqK+GN22HpveHbq0pg5b/c0nciXPUEZAzyJMTuTNWgIiIiIiIiXsn9BP5+euOEuNFxa+EfZ0Luuq6JqwdRTbGIiIiIiIgX9q+Ff50Dh4uD20adAVM+C4NnQNEu2PgSLL0P/DVQshf+eTZ87mkYMtO7uLsZJcUiIiIiIiJdrWgXPHpZMCGOTYK5P4fjroO6rne9hsCw2S5RfuIa15z6cDE8/SX4xhJISPMu/m5EzadFRERERES6UnkBPHIplOxz6wnpcN2rcPz1wYQ41MjT4UsvQ1KWWy/eDQt/1nXxdnNKiqXL3X777Rhj6pc777yz1XO2bt0ads64cePC9m/fvr1+3+23395JkYuIiIiIHCVr4ZnrIW+jW/fFwRWPQP8pLZ/XbxKc86vg+rK/w84lnRdnD6KkWDz36KOPtnrMI4880gWRiIiIiIh0spX/gk8XBtcvuQ9GnNq2cydd7qZnAsDCf7/lRq6Wo6KkWDwTGxtLcnIy69atY9WqVS0eW5c4p6end0FkIiIiIiKdoHA7vHprcH3WN2HSZW0/3xg47/cQn+rW8zbBigc6NMSeSEmxeCYmJoYLL7wQaLm2eNmyZWzatInU1FTmzp3bVeGJiIiIiHQcvx+e+wZUl7n1nDHwmVtbPqcpvQaHn7f0PvDXdkyMPZSSYvHU1VdfDcDjjz+O3+9v8pi6ptOXXHIJycnJXRabiIiIiEiH+fBB2PGeK5sYuPg+iEtq37WmfyE46FbRTjdtk7SbkmLx1Ny5c8nJyWHPnj0sWrSo0f6amhqeeOIJAD73uc91cXQiIiIiIh2gshje/EVw/aRvw6Dp7b9eXJJLjOssua/91xIlxeKt2NhYrrjiCqDpJtSvvfYaBw4coG/fvpxxxhldHZ6IiIiIyNF77/dQnufKGYPhlB8c/TWPvx58sa684z3Y9/HRX7OHUlIsnqurAX7mmWeorAwfPa+u6fSVV15JTExMl8cmIiIiInJUCnfAB38Nrs/5KcQlHv11MwbCMRcH11Vb3G5KisVzs2bNYuTIkRw6dIgXXnihfntpaSnPP/88EOx7LCIiIiISVRb+DGoPu/KAaTDx0o679glfC5bXPg1leR137R4k1usAot2khyZ5HUKnWXPtmi6711VXXcUdd9zBI488wmWXuWHpFyxYQHl5OWPHjuW4447rslhERERERDrEvo9dslpn7i/B14H1koOOg4HTYc9KqK2CDS/C9Gs77vo9hGqKJSLU1QS//PLLFBYWAsGm0xpgS0RERESi0tu/DpbHnQ9DZ3X8PUJrntf/r+Ov3wMoKZaIMGbMGI477jiqqqp46qmn2LdvH2+++SbgapFFRERERKJK7jrYEOwayGm3dM59xp0fLG9dBBVFnXOfbkzNp49SVzYx7u6uvvpqVqxYwSOPPEJpaSm1tbX1/Y1FRERERKLKu78LlseeB/0mds59ModC/6mwbxX4q2HzazB5fufcq5tSTbFEjLoRpt977z3+9Kc/ARpgS0RERESiUN5mWLsguH7q9zv3fuMvCJbX/7dz79UNKSmWiFE3F7G1lu3btxMXF8f8+fqWS0RERESizLu/A6wrjzoTBhzbufcbf2GwvPkNqCrv3Pt1M52SFBtjLjPG/MkY864xptgYY40xjzRz7GhjzA+NMW8aY3YZY6qMMbnGmOeNMad3RnwSuUJrhufOnUtOTo6H0YiIiIiIHKHivbDmqeD6KZ1cSwzQewzkjHXlmgr4dGHn37Mb6aw+xbcCU4BSYDcwroVj7wCuAD4BXgIKgLHAhcCFxpibrLX3dFKcEmHmz59fP/1S7969PY5GREREROQILfs7+GtceciJMGRm19z3mAvhnd+48if/DW9SLS3qrKT4O7hkeAtwKvBWC8e+AvzKWvtR6EZjzKnA68BvjDFPWWv3dVKsEkHi4+MZN66l71Bat3v3bpYsWdLiMVlZWYwZM+ao7iMiIiIiEqaqHFb+K7g+6+tdd+/xFwST4s2vgd/fsXMid2OdkhRba+uTYGNMa8c+2Mz2t40xi4AzgROBZzouQunOHnjgAR544IEWj7nooot47rnnuiYgEREREekZVv8HKgpduddQGHtu192732RI6Q1lB6GyCA6sg36Tuu7+USzSp2SqDjzWtOVgY8zKZnYdXdWjiIiIiIhIS/x+WHJvcH3mDeCL6br7GwPDToJ1z7r17e8pKW6jiK1PN8YMBeYA5cA7HocjHej222/HWktlZeURn/vggw9irWXDhg1h24cNG4a1ts2LaolFREREpEN9+ibkbXLl+DQ41oOpRYedFCxvf6/r7x+lIrKm2BiTADwKJAA/sNYWtuU8a+30Zq63EpjWcRGKiIiIiIiEWPa3YHnaNZCY3vUxDA1JincsVr/iNoq4V8gYEwM8DMwGngB+621EIiIiIiIiLSjcAZtfD67P+LI3cfQeC8mBKU0rCuHAJ97EEWUiKikOJMSPAJcDTwJXW2utt1GJiIiIiIi04MOHgEDaMnIOZI3wJo66fsV11IS6TSImKTbGxAKPA1cCjwFXWWvbNMCWiIiIiIiIJ2qq4MOHg+vHfcm7WKBBUvyud3FEkYhIio0x8cDTuBrifwPXWGtrvY1KRERERESkFRtfhLIDrpzWH8ac7W08oUnxjvddv2JpkedJcWBQrWeBi4AHgC9aa/WTExERERGRyLfin8HytGshxuOxjHuPg+RsV64ogIPrvY0nCnTKT8wYczFwcWC1X+BxljHmwUA5z1r7vUD5PuBcIA/YA/zEGNPwkoustYs6I1YREREREZF2ydsC2wKzxxofTPu8t/FAsF/xJ8+79e3vQd8J3sYU4Trra4ypwLUNto0ILAA7gLqkeHjgMQf4SQvXXNRBsYmIiIiIiBy9j0L6Eo85GzIGehdLqKEhSfHOJTDzq97GE+E6JSm21t4O3N7GY0/rjBhEREREREQ6jb8WVj8RXI+EWuI6g6YHy/tWeRZGtPC8T7GIiIiIiEjU2foWlOxz5ZTeMOoMb+MJ1WcC+AL1nwVbofKQt/FEOCXFIiIiIiIiR2rVY8Hy5CsgJs67WBqKS4Q+44Pr+z72LpYooKRYRERERETkSFQUwfoXgutTPutZKM3qPzVY3vuRZ2FEAyXFIiIiIiIiR2LdAqg97Mr9JkO/id7G05QBU4Plvau8iiIqKCkWERERERE5EqFNp6d+zrs4WtL/2GBZg221SEmxiIiIiIhIW+Vtht3LXdkXB5Mu9zae5vTVYFttpaRYRERERESkrUJricfMhZRs72JpSVwi9NZgW22hpFhERERERKQt/LXw8X+C61Ov8i6WthgwJVhWv+JmKSkWERERERFpi62LoGSvKyfnwOizPA2nVQPUr7gtlBRLl7v99tsxxtQvd955Z6vnbN26NeyccePGtXrOQw89VH/84MGD8fv9rZ7z4IMPht2nbomJiSE7O5sTTzyRO+64g7y8vDY9VxERERHpRsLmJp4fWXMTNyV0sC3VFDdLSbF47tFHH231mEceeeSIrxt6zu7du1m0aNERX6OO3++noKCADz74gJ/85CdMmDCBJUuWtPt6IiIiIhJlKg/BhpC5iSO96TQ0GGzrUw221QwlxeKZ2NhYkpOTWbduHatWrWrx2LrEOT09vU3X3rt3L2+++WbYtocffviI4nvppZcoKSmhpKSEoqIiPv74Y2644QYADhw4wIUXXkhRUdERXVNEREREotS6Z6Gm0pX7TXJLpGs02NZq72KJYEqKxTMxMTFceOGFQMu1xcuWLWPTpk2kpqYyd+7cNl37sccew+/3Y4zhnHPOAeCZZ56hoqKizfElJSWRmppKamoqGRkZTJ48mXvvvZfrrrsOgIMHD3L//fe3+XoiIiIiEsVWPR4sR+rcxE3pPzlYPrDeuzgimJJi8dTVV18NwOOPP95sn9+6ZtCXXHIJycnJbbpuXa3wSSedxI9//GMASkpKeP755482ZG677bb68sKFC4/6eiIiIiIS4Yp2wa5A1zkTAxMv8zaeI9E7ZCyegxu8iyOCKSkWT82dO5ecnBz27NnTZJ/fmpoannjiCQA+97m2fSO3Zs0aVq9eXX/OiSeeyPDhw4H29U1uaOjQoaSmpgKur7KIiIiIdHPrFgTLI06D1N6ehXLEeo8Nlg9u9C6OCKakWDwVGxvLFVdcATTdhPq1117jwIED9O3blzPOOKNN16yrJY6Pj2f+/PkYY7jqKjcQwquvvsqBAweOOm6fz/3qWGuP+loiIiIiEuHWPhMsT7zUuzjaIywpVk1xU5QUi+fqaoCfeeYZKisrw/bV1exeeeWVxMTEtHotv9/PY4+5ofLPPfdcMjMzgWAz7ZqaGv7zn/80e35b7N27l+LiYgAGDBhwVNcSERERkQiXtwX2fezKMfEw/nxv4zlSGUMgNsmVy/OgLN/beCKQkmLx3KxZsxg5ciSHDh3ihReCw9yXlpbW9wGuS2pb89Zbb7Fnz55G54wbN47p06cDR9+E+q677qovn3baaUd1LRERERGJcKG1xKPPgsQM72JpD58Peo8JruepCXVDsV4HEPVuj7JfiiNxe9fNY3bVVVdxxx138Mgjj3DZZW7gggULFlBeXs7YsWM57rjj2nSduqbTGRkZnH9++Ld4V199NStXrmT58uVs3LiRsWPHNnWJJvn9fnbs2MF9993Hn//8Z8BND/WVr3ylzdcQERERkShjLax9Org+cZ53sRyN3uOCtd0HN8DQE72NJ8KoplgiQl2t7ssvv0xhYSEQrNFt6wBbFRUVLFjgBkG47LLLSEhICNsf2gS7LbXFp59+OsYYjDHExMQwYsQIfv3rX2OtJT09naeffpo+ffq07QmKiIiISPTJXQt5m1w5LgXGnO1tPO2lwbZapKRYIsKYMWM47rjjqKqq4qmnnmLfvn28+eabAPWDZLXmueeeo6SkBGi6uXW/fv2YM2cO4JLiIx0kKy4ujmOOOYbvfve7rFmzhjPPPPOIzhcRERGRKBPadHrsORCf4l0sR0PTMrVIzaePVhc2Me7urr76alasWMEjjzxCaWkptbW19f2N26Ku6XRmZiYZGRmsWrWq0TEzZ87ktddeY/v27bz33nucfPLJzV7vpZdeqt8fExNDUlLSkT8pEREREYlO1oYnxZOiaG7ihsKSYtUUN6SkWCLGlVdeyf/93//x3nvvsWvXLqDtA2wdOHCA119/HYDCwkKmTZvW6jmPPPJIi0lxUlJS/XzEIiIiItLD7F4BRTtdOTEDRn7G23iORq+hEJMAtYehZB9UHoq+AcM6kZpPS8Som4vYWsv27duJi4tj/vz5bTr38ccfp6am5oju9+STT3L48OH2hCoiIiIi3V1oLfH4CyA2ofljI11MLGSPCq4f3ORdLBFISbFElNCa4blz55KTk9Om8+qaTo8bNw5rbYvLyy+/DEBRUREvvvhixz8JEREREYlu/lpYtyC4PjGKm07XCRtsS/2KQ6n5tESU+fPn10+/1Lt37zads2HDBlauXAnAZz/72VaPP+OMM+jduzcHDx7k4YcfZt68KB1aX0REREQ6x47FUJrryim9YVjzXe6ihgbbapZqiiWixMfHM27cOMaNG0d2dnabzqmrJQbXL7k1sbGx9XMhv/TSSxQUFLQvWBERERHpntaEzE084RLX/DjaaVqmZikplqhmreWxxx4DYPr06YwZM6ZN59XVKFdVVfHkk092WnwiIiIiEmVqqmD9f4PrEy/1LpaOpBGom6WkWKLau+++y/bt24G21RLXOemkkxg8eDAQXtMsIiIiIj3c1kVQUejK6YNg0AxPw+kwWSPAF6jxPrQTqsq8jSeCGGut1zF0OmPMymnTpk2r63faFuvXrwdg/PjxnRWW9DB6T4mIiIhEgQVfgdVPuPKJN8JZd3gbT0e651go2OrKX3sf+k7wNp6OZ9pzkmqKRUREREREAKorYEPI7CTdpel0nczhwXLBNu/iiDBKikVERERERAA2vwZVpa6cNRL6T/E2no6WFZIUFyoprqOkWEREREREBMJHnZ50GZh2tcaNXKopbpKSYhERERERkcpiV1Ncp7s1nQbVFDdDSbGIiIiIiMjGl6Gm0pX7Tgqf17e7UE1xk5QUi4iIiIiIrA1pOj1xnndxdKbMYcHyoV1QW+NZKJFESbGIiIiIiPRs5QXw6ZvB9e6aFMcnQ2o/V/bXuMRYlBSLiIiIiEgP98nzLkkEGHR8eI1qd6N+xY0oKRbpAtZar0MQERERkeasfSZY7o4DbIVSv+JGOiUpNsZcZoz5kzHmXWNMsTHGGmMeaeWcE40xLxljCowx5caY1caYbxtjYjojxtaYwPDrfr/fi9tLN1OXFJvuNqy/iIiISLQr2Q/b3wusGDjmYi+j6XyqKW4ktpOueyswBSgFdgPjWjrYGHMR8AxQCTwBFAAXAH8AZgOXd1KczYqJiaGmpoaamhri4+O7+vbSzVRXVwPufSUiIiIiEWTds0CgVd+wkyC9v6fhdDrVFDfSWc2nvwOMAdKBr7V0oDEmHfg7UAucZq29zlr7fWAq8AFwmTHmyk6Ks1nJyckAlJaWdvWtpRsqKysDgu8rEREREYkQPanpNDSoKd7uWRiRpFOSYmvtW9bazbZtHSkvA3oD/7HWrgi5RiWuxhlaSaw7Q0pKCgCFhYXU1tZ29e2lG6mtraWwsBAIvq9EREREJAIUbofdy13ZFwvHXORpOF0ia0SwXLANNPZNpzWfPhKfCTy+0sS+d4By4ERjTIK19nBLFzLGrGxmV4vNt5uSlpZGfn4+VVVV7Nq1i+zsbFJSUjDGqF+otMpai7WWsrKy+vdRfHw8aWlpXocmIiIiInXWLgiWR34GkrO8i6WrJGVCQgYcPgTVZVB6ANL6eh2VpyIhKR4beNzUcIe1tsYYsw2YAIwA1ndVUDExMQwePJjt27dTUVHB7t27u+rW0g3VvZ/Up1hEREQkgoQmxT2h6TSAMZA1DPZ97NYLtykp9joAICPweKiZ/XXbe7V2IWvt9Ka2B2qQpx1pYPHx8YwYMYJDhw5x6NAhqqqqNLWOtJkxhvj4eDIyMsjIyCA2NhJ+3UREREQEgIMbIXeNK8cmwthzvY2nK2UODybFBdtgyAnexuOxaPiUXtdW2ZNsNDY2luzsbLKzs724vYiIiIiIdIbQAbZGnwWJ6d7F0tU0LVOYzhp9+kjU1QRnNLM/vcFxIiIiIiIi7Wdtzxt1OpSmZQoTCUnxxsDjmIY7jDGxwHCgBtjalUGJiIiIiEg3te9jyN/iyvGpMGaut/F0NU3LFCYSkuI3A49nN7HvFCAZeL+1kadFRERERETaJLSWeNx5EJfkXSxeyBgcLBfv8S6OCBEJSfHTQB5wpTHmuLqNxphE4OeB1Xu9CExERERERLoZvx/WPRtcn3iZd7F4JX1AsFyyD2prvIslAnTKQFvGmIuBiwOr/QKPs4wxDwbKedba7wFYa4uNMV/GJceLjDH/AQqAC3HTNT0NPNEZcYqIiIiISA+zexkc2uXKSZkw4jRPw/FEbAKk9oXSXLB+lxj3Gtz6ed1UZ40+PRW4tsG2EYEFYAfwvbod1trnjDGnAj8GLgUSgS3Ad4F7rOZBEhERERGRjhDadHr8hRAb710sXsoY5JJigEO7lRR3NGvt7cDtR3jOYqAHTQ4mIiIiIiJdqrYmvOn0pB7YdLpO+kDYs9KVD+32NhaPRUKfYhERERERkc63/V0oO+jKqf1g6Gxv4/FS2GBbSopFRERERES6v9Cm0xMuAV+Md7F4LWNQsKyaYhERERERkW6u5jCs/29wfeKl3sUSCZQU11NSLCIiIiIi3d+nb0LlIVfuNQQGHdfy8d1dxsBg+VDPnqtYSbGIiIiIiHR/oU2nJ14KxngXSyQI7VNcN0VVD6WkWEREREREureqctjwUnC9pzedBkjOgZgEV64sgsOlnobjJSXFIiIiIiLSvW16GarLXDlnDPSd6G08kcDng/QBwfXintuEWkmxiIiIiIh0b2ueDpYnXa6m03XCBtvquU2olRSLiIiIiEj3VV4Am18PrqvpdFBYv+KeOwK1kmIREREREem+1v8X/NWuPPA4yB7pbTyRRCNQA0qKRURERESkO2vYdFqCNFcxoKRYRERERES6q0N7YPt7rmx8MOESb+OJNOpTDCgpFhERERGR7mrdAsC68vBTIa2vp+FEnNA+xRp9WkREREREpJtZ81SwrKbTjaU36FPs93sXi4eUFIuIiIiISPdzcBPs+9iVYxJg/PnexhOJElIhsZcr1x6G8jxPw/GKkmIREREREel+1oYMsDVmLiRmeBdLJNO0TEqKRURERESkm7FWTafbKmxaJiXFIiIiIiIi0W/vh1Cw1ZUT0mH0Wd7GE8k0LZOSYhERERER6WZC5yYefyHEJXoXS6RLHxAsl+zzLg4PKSkWEREREZHuw18La58Jrk+6zLtYokFqv2C5ZL93cXhISbGIiIiIiHQf29+F0lxXTukDw0/xNp5IlxaSFJcqKRYREREREYluq58MlideCr4Y72KJBmmqKVZSLCIiIiIi3UNVGXzyfHB9skadblVa/2C5JNe7ODykpFhERERERLqH9S9AVakr54yFAdO8jScaJGVCTLwrHz4EVeXexuMBJcUiIiIiItI9fPx4sDzlSjDGu1iihTGQ2je43gP7FSspFhERERGR6Fe8F7YuCqwYmDzfy2iiSw/vV6ykWEREREREot/qJwDrysNPgYxBnoYTVUJripUUi4iIiIiIRBlr4eP/BNenXuVdLNEobLAtJcUiIiIiIiLRZd8qOLjBleNSYNz5noYTddLUp1hERERERCR6hdYSH3MhJKR6F0s0Uk2xiIiIiIhIlKqpgjVPBdenXOldLNEqVQNtiYiIiIiIRKctb0B5viunD4RhJ3sbTzTS6NMiIiIiIiJRKnRu4slXgC/Gu1iiVWhSrD7FIiIiIiIiUaK8ADa9ElxX0+n2ScoCX5wrVx6C6gpv4+liSopFRERERCQ6rVsAtVWuPGAa9B7rbTzRyufr0XMVKykWEREREZHoFDrq9JTPehdHd9CD+xUrKRYRERERkehzYD3sXu7KvliYeKm38US7HtyvWEmxiIiIiIhEnw8fDpbHnQcp2d7F0h2opjgyGGPOM8a8ZozZbYypMMZsNcY8ZYyZ5XVsIiIiIiISIWoOh486Pe3z3sXSXfTguYojJik2xvwKeAGYBrwC3A18CFwELDbGXO1heCIiIiIiEik2vAAVBa6cMRhGnO5tPN1BD64pjvU6AABjTD/ge0AuMNlaeyBk3+nAm8DPgEe8iVBERERERCLGh/8Olo+9RnMTdwT1KfbcUFwsS0MTYgBr7VtACdDbi8BERERERCSCFG6HrYsCKwaO/ZyHwXQjmpLJc5uBKmCGMSYndIcx5hQgDXjDi8BERERERCSCfBTSeHTUGZAxyLtYupO0/sFyD0uKI6L5tLW2wBjzQ+D3wCfGmOeAfGAkcCHwOvDV1q5jjFnZzK5xHRSqiIiIiIh4pbYmPCnWAFsdJznbTW3lr4HKIqiugLgkr6PqEpFSU4y19o/APFyi/mXgZuByYBfwYMNm1SIiIiIi0sNseQNK9rlySm8Ye4638XQnPl94E+rS3PpiVW0VHx34yIOgukbEJMXGmB8ATwMP4mqIU4DpwFbgUWPMr1u7hrV2elMLsKETQxcRERERka4QOsDW1KsgJs67WLqjsH7FLineW7qXa1++lutfvZ71+es9CqxzRURSbIw5DfgV8F9r7XettVutteXW2g+BS4A9wP8ZY0Z4GKaIiIiIiHilZD9seiW4fqyaTne4lJCxjcvzeGf3O1z+v8tZm7+WKn8V3130Xcqqy7yLr5NERJ9i4PzA41sNd1hry40xy3DJ8bG4mmMREREREelJVj0KttaVh54EOaO8jac7CkmK31z/BDcVB5tMx5pYrhp/FcmxyV5E1qkiJSlOCDw2N+1S3faqLohFREREREQiid8PHz4cXNcAW50jJTgR0Nqdi6BXBgB9kvvwu1N/x9Q+U72Jq5NFRPNp4N3A41eMMQNDdxhjzgFmA5XA+10dmIiIiIiIeGz7u1C4zZUTMuCYC72Np5vabQ/Xl7NqXa38Cf1P4Mnzn+y2CTFETk3x07h5iM8A1htjngX2A+NxTasNcLO1Nt+7EEVERERExBPL7g+WJ8/vMVMFdZVafy0PrH2A7Zuf5peBbdm1fm6YcgM3TL6BGF+Mp/F1tohIiq21fmPMucA3gCtx/YeTgQLgJeAea+1rHoYoIiIiIiJeKNoFG18Krh9/vXexdEN5FXnc8u4tLNm3hFkh7YjHxg5hZP/Pd/uEGCIkKQaw1lYDfwwsIiIiIiIisOIBsH5XHn4q9BnnbTzdyPt73+eWd2+hoLIAgIKYYAJcVVjG2X94hxnDs7hpzmhmj8pp7jJRL1L6FIuIiIiIiISrroSVDwXXZ3zFu1i6kRp/Dfd8eA83vH5DfUJsrWHfoZPrj8kxhwBYtq2Aax5YypPLd3kSa1eImJpiERERERGRMGufgQqXtJExGMae42083cD+sv384J0f8NGB4HRL/ppUKvdcQWX5cEh8CoAsSvDhx48Pv4WbF6xmYGZSt6wxVk2xiIiIiIhEHmth2d+C68dfBz2gf2tnenPnm1z2v8vCEuKa0lGUb72J2vLR1BBLoU0FwGcsmZTUH+e3cM/CzV0ec1dQTbGIiIiIiESe3cth38euHJsI0671Np4oVl5dzq+X/5pnNj9Tv81nYqjIPYOq/FMJrSvNt+lkmlIAsk0x+Tajft/SbQVsyi1hTN+0Lou9K6imWEREREREIk/oNEyTLoPkLO9iiWJr89Yy/4X5YQlx3+S+XD7gF1Tln07DlDCf9PpytiludL3FW/I6LVavKCkWEREREZHIUpIL654LrmuArSNW66/l/tX3c81L17CjeEf99jOHnskzFz5DhhnT5Hl5NpgU53Co0f7SypqOD9Zjaj4tIiIiIiKRZeWD4K925cEnQP8pnoYTbfaU7uFH7/6IDw98WL8tOTaZH838EReOvBBjDKmJBU2eG9pcuqma4tTE7pdCdr9nJCIiIiIi0aumClb8M7g+48vexRJlrLW8sPUFfrn0l5RWl9Zvn9J7CneefCeD0wbXb2tuFOl823Lz6e44+rSSYhERERERiRwb/gel+105tR+Mv9DbeKJEUWURv1j6C17Z/kr9thgTw1enfJUvT/oysb7w1G9M3zRmDM9i2bbwGuOwPsUNmk/PHJ7V7QbZAvUpFhERERGRSLLkvmD5uC9CbLx3sUSJRbsWccl/LwlLiAenDeahcx7ia1O+1ighrnPTnNH4TPi2vJDm0zkhNcU+AzfOGd2hcUcKJcUiIiIiIhIZdi6F3ctc2RcH07/obTwRrqSqhFvfu5Vvvfkt8iqCo0JfMuoSnrrgKab0brkv9uxROdw5b1JYYtxU82mfgbvmTe6WTadBzadFRERERCRSvH9PsDz5Ckjr610sEe79Pe/zk/d/Qm55bv227MRsbj/xdk4bfFqbr3PF8UMYlJnMPQs3s3RbAXmEDLRFMTOHZ3HjnNHdNiEGJcUiIiIiIhIJ8j+FDS8G10/8pnexRLDy6nJ+t+J3PLnpybDt5ww7hx/N/BG9Ensd8TVnj8ph9qgcNuWWsHz9Vljktg9OKOOJr846+qAjnJJiERERERHx3gd/Aawrjz4L+oz3NJxItHz/cm5bfBt7SvfUb+uV0ItbT7iVucPmHvX1x/RNY0yfyfBOHPiriakuheoKiEs66mtHMiXFIiIiIiLirbI8WPVocP3Eb3kXSwQqrSrljx/+kSc2PhG2/TODP8Nts24jJ6kDmzYbAym9oWSvWy/Lg16DWz4nyikpFhERERERby37O9RUunL/KTDsZG/jiSDv7H6Hn33ws7C+w2lxadwy8xbOH3E+xpgWzm6nlJyQpPiAkmIREREREZFOc7gEloZMw3Tija62socrrCzkV8t/xYtbXwzbfuqgU7n1hFvpl9Kv826e0jtYLstr/rhuQkmxiIiIiIh4Z8U/obIIgOKkwfw7dwIpxduYPSqHMX3TvI3NA9ZaXtn+CncuvZPCw4X12zMTMrll5i2cPezszqkdDhWWFB/s3HtFACXFIiIiIiLijeoKqt69h/jA6i+Kz+aJN7bW754xPIubuvl0QKH2l+3nF0t+waLdi8K2nzfiPH54/A/JTMzsmkBSQl7vHpAU+7wOQEREREREeqaVz/2J+ErXPHefzeLZ2pPC9i/bVsA1DyzlyeW7vAivy9T6a3ls/WNc8vwlYQlx3+S+/GXOX7jr5Lu6LiEGNZ8WERERERHpbO9v2seQtX+DQEvg+2vOo4q4Rsf5Ldy8YDUDM5O6ZY3xJ/mf8LMPfsa6/HVh268YewXfnvZtUuNTuz4oNZ8WERERERHpXB+/eB8nGlcLmW/T+E/t6c0e67dwz8LN3SopLqsu488f/ZnHNjyG3/rrtw9LH8ZPZ/2U4/od511wSopFREREREQ6z6a9+Zxf+Gh9Z84Has6lgsQWz1m6rYBNuSVRP/iWtZaFOxdy57I7OVB+oH57vC+e6ydfz3UTryM+Jr6FK3SBVCXFIiIiIiIinebgu/9kts8lW/k2jYdqz2rTeYu35EV1Ury3dC+/XPpL3t79dtj2E/qfwK0n3MrQ9KEeRdZAckiNfKmSYhERERERkY5TU8Wkrf+oX72/5nzKSGrTqaWVNZ0VVaeqqq3ioXUP8fc1f6eipqJ+e1ZiFj84/gecO/zczp9m6UgkZwfLFQVgbbeeO1pJsYiIiIiIdJ2PHib98H4A8mw6/649s82npiZGX/ryzu53+NWyX7GzZGfY9svHXM5N024iIyHDo8haEJ8MsUlQUwG1VVBVBgkeDPjVRaLvXSUiIiIiItGpugLe/V396n01F7TalzhUNA20tatkF79e9utGcw6PyRzDbSfcxtQ+Uz2Jq82Ss6B4jytXFCgpFhEREREROWrL7q9PtIp8mTxSe0abT505PCsq+hNX1FTwz7X/5J9r/kmVv6p+e1p8Gt+c+k3mj51PrC8K0rCkkKS4PB96DfE2nk4UBT8NERERERGJehVF8O7v61fzp3+bqvcSwLZ+qs/AjXNGd15sHcBay5s73+TXy3/N3rK9YfvmjZ7HjcfeSHZSdjNnR6DkzGC5vMC7OLqAkmIREREREel8i/8IlUWunDmckWd/gzv77OOWBWvwt5AY+wzcNW9yRDed3liwkd+s+A1L9y0N2z4hewI/nvljJvWe5FFkRyFssK1C7+LoAkqKRURERESkcxXvgyX3Bdc/cyvExHHF8UMYlJnMPQs3s3Rb49rImcOzuHHO6IhNiPMr8vnzqj+zYPMC/NZfv71XQi9umnYT80bPw2d8HkZ4FJKygmXVFIuIiIiIiByFRb90IxkD9JsME+bV75o9KofZo3LYlFvC4i15lFbWkJoYy+xRORHbh7iqtopH1j/C/avvp6y6rH57jInhsjGX8a1jvxWZo0ofieTQpDjfuzi6gJJiERERERHpPPtWw4cPB9fPuB18jWtPx/RNi9gkuI61ljd2vsHvV/ye3aW7w/adOOBEvn/c9xmVOcqj6DpYaE1xhWqKRUREREREjpy18OqPqB9Na9SZMGqOpyG117q8dfxmxW9YmbsybPvwjOF877jvcfLAkzHGeBRdJwjtU6zm0yIiIiIiIu2w4UXY/q4rmxiY+wtv42mHXcW7uOeje3hl+yth29Pj0/n61K8zf+x84nxxHkXXiZJVUywiIiIiItJ+NYfhtVuD68dfD73HehfPEcqvyOdvq//GUxufosbW1G+PNbFcOe5KbphyQ/T3G25JkvoUi4iIiIiItN8Hf4bCba6c2AtOu9nTcNqqvLqcf3/yb/619l+U15SH7TtjyBncOO1GhmcM9yi6LhQ2T7GmZBIREREREWm7wh3w9m+C66fdEt4cNwJV+6t5dvOz3PvxveRV5IXtm9ZnGt+Z/h2m9pnqTXBeCJunWM2nRURERERE2u6Vm4NTMPWd5JpORyhrLQt3LuTuD+9me/H2sH0jM0by7enf5tRBp3avQbTaIiEdfLHgr4GqUtccPjbB66g6RcQlxcaYk4FvAycCWUABsAb4o7X2JQ9DExERERGR1mx4CTaGfGw///cQE3FpBwBL9y3lno/uYfXB1WHb+yT34ZtTv8kFIy8g1heZsXc6YyApE8oOuvXyAkjv721MnSSifsLGmFuBO4A84AVgH5ADHAucBigpFhERERGJVIdL4eUfBtenfR4Gz/AunmZ8mPshf171Z5bvXx62PS0ujesmXcdV468iKTbJo+giSFJWMCmuUFLc6Ywxl+MS4jeAedbakgb7u+E45yIiIiIi3cibd8Chna6clAVn/D9v42lgzcE1/HnVn3l/7/th2+N8cVw17iqun3Q9vRJ7eRNcJOohcxVHRFJsjPEBvwLKgasaJsQA1trqLg9MRERERETaZucSWPq34PrcX0bM4Frr89fzl1V/4e3db4dtjzWxXDTqIr46+av0T+2etaBHJblnTMsUEUkxrv/wcOBpoNAYcx4wEagElllrP/AyOBERERERaUF1BTz/DcC69VFnwJQrPQ0JYHPhZv666q+8sfONsO0+4+P8Eedzw5QbGJw22KPookBSyLRM3XgE6khJio8PPOYCHwKTQncaY94BLrPWHmzpIsaYlc3sGnfUEYqIiIiISNMW3Qn5W1w5Pg3O/6MbqMkj2w5t495V9/LK9lewdYk6YDCcPfxsvjblaz1jruGjFVZTrKS4s/UJPN4AbAPOAJYCQ4HfAXOBp3CDbYmIiIiISKTYvhgW3xNcP/P/QS9val83FW7iH6v/was7XsVv/WH7zhhyBl+f+nVGZ472JLaopD7FXSom8GhwNcIfB9bXGWMuATYBpxpjZrXUlNpaO72p7YEa5GkdGbCIiIiISI9XeQie/Sr1zaaHnwrTv9jlYazLW8f9q+/nzV1vNtp36qBT+cbUbzA+e3yXxxX1kkJqitV8utMVBh63hiTEAFhrK4wxrwLXATMA9S8WEREREYkEL34PDu1y5cRecPG94PN12e0/zP2Q+9fcz+I9ixvtmz1gNl+f+nUm957cZfF0O2o+3aU2Bh6LmtlflzRrsjARERERkUiw+klY82Rw/YK7IWNgp9/WWsuSfUu4f/X9rMhd0Wj/ZwZ/hq9M/goTciZ0eizdXmjzadUUd7p3gBpgtDEm3lpb1WD/xMDj9i6NSkREREREGjuwAf53U3B96udgwsWdektrLe/sfof7V9/P6rzVYft8xsfcoXO5fvL1jMkc06lx9ChJmpKpy1hr84wxTwCfA34C3Fq3zxhzJm6grUPAK95EKCIiIiIiABwuhSc/D9Xlbj17NJzzq067XbW/mle3v8qDax9kY+HGsH2xJpbzR57PdROvY1jGsE6LocdS8+ku911gJvBjY8wpwDLc6NOXALXAl621Rd6FJyIiIiLSw1kLL3wb8gLJaWwSzP83JKR1+K3Kqst4ZtMzPLL+EfaV7QvbF+eLY97oeXxx4hcZmNr5TbZ7rMRewXLlIfDXgi+m2cOjVcQkxdbaA8aYmbha4kuAE4AS4EXgTmvtEi/jExERERHp8d7/E6x5Krh+/h+g7zEdeou8ijweXf8oT2x8gpKqkrB9SbFJXD7mcq6dcC19kvs0cwXpMDGxLjGuLAIsVBRBSnbL50ShiEmKAay1Bbga4+96HYuIiIiIiITY9Cq8/pPg+rRrYepnO+zyWw9t5aF1D/G/T/9Htb86bF9WYhafHfdZrhx7Jb1Cay+l8yVnBZJiXL9iJcUiIiIiItLjHFgPT19H/XzEQ2bBub856staa/nowEf8a92/WLRrUaP9Q9KGcO2Ea7lw5IUkxiYe9f2kHZKygK2u3E1HoFZSLCIiIiIizSveC4/Oh7qmzBlDYP7DEJvQ7ktW+6t5Y8cbPLL+EVYfXN1o/+Tek/nihC9y+uDTiemGfVijSg8YbEtJsYiIiIiINK2iEB65FA7tdOvxqXDVfyC1d7suV1BZwNObnuaJDU9woOJAo/2nDTqNL078Isf2ORZjzNFELh0ldK7ibjotk5JiERERERFprKocHrsSDnzi1n2xcPlD0HfCEV9qY8FGHl3/KC9ufZEqf1XYvjhfHBeMvIBrj7mWEb1GdETk0pFC5ypW82kREREREekRqivhic/BrpAJYC6+F0af0eZL1PprWbR7EY+uf5Tl+5c32p+TlMP8sfO5fMzl5CTldETU0hmSM4NlNZ8WEREREZFur7oS/nMVfPpmcNvcX8Lk+W06vbiqmGc3P8vjGx5nT+meRvsnZE/gc+M/x9nDziYuJq6jopbOoppiERERERHpMarK4Ymr4dOFwW2n3QKzvtHqqevy1/Hkxid5aetLVNZWhu2LMTGcMfQMrh5/NVN6T1F/4WgS1qdYSbGIiIiIiHRX5QXw+JWwa2lw26k3w2k3N3tKRU0Fr2x7hSc3Psna/LWN9mckZHDZ6Mu4ctyV9Evp1xlRS2cbdhJ84UVXY5za1+toOoWSYhERERGRnu7Qbnh4HuRtDG477ZZmE+Jth7bx5MYnef7T5ympm6opxJjMMXx23Gc5b8R5JMUmdVbU0hVSciDlJK+j6FRKikVEREREerLdK1yT6ZJ9gQ0Gzr4LTrgh7LBqfzVv7XyLJzc+ydL9SxtdJs4Xx9xhc7li7BVqIi1RRUmxiIiIiEhP9dGj8MK3oTYwTZIvDub9DSZeWn/IrpJdPLv5WZ7b8hwHKw42usSg1EHMHzufi0ddTGZiZqP9IpFOSbGIiIiISE9TXQGv/hhWPBDclpTp5iEecSqHaw+zcMdCFmxe0GStsM/4OGXQKVw59kpmDZiFz/i6MHiRjqWkWERERESkJ8ldB09/CQ5uCG7rcwxc+RgbqWLB0jt5YesLFFcVNzo1JymHeaPncdnoy+if2r8LgxbpPEqKRURERER6gtpqWHw3vP1rqD1cv7lm3Hn8d+LZPPn+LazLX9foNJ/xMXvAbOaNnsepg07V3MLS7SgpFhERERHp7navgP/eCAeCSW9tbAL/HX0id1ZvpmLlmkanDEwdyCWjLuGiURdpOiXp1pQUe62iEF67Dcrzwfjgyke9jkhERESkVZtyS1i8JY/SyhpSE2OZPSqHMX3TvA5LGiraBQt/BmueDNu8OTGF/8tOZ1vlp2Hb43xxnDHkDOaNmceMfjPUV1h6BCXFXjMx8NHDrqw53ERERCTCLd6Sx90LN7NsW0GjfTOGZ3HTnNHMHpXjQWQSpngffPBnWPb3sKbSFcbw58wMHk1PozZkyqTRmaO5dPSlnDf8PHol9vIgYBHvKCn2WkIaxMS7YfBrKqCqDOJTvI5KREREpJEnlu/klgVr8Num9y/bVsA1DyzlrnmTmX/84K4NTpyDG2HpfdiPHsHUTbMUsDA5id9mZbI7zqUA6fHpnDP8HC4edTETsidoXmHpsZQUe80YSM6Bkr1uvSxPSbGIiIhEnMVb8lpMiOv4Ldy8YDUDM5PaXmPs90NlketWVl7gupVVFMDhUqipdDWdNVXusbbadTkzPvDFgi/GtbyLTXCVDfGpkJAaeEyHlGxI6d29P19VlcHGl7Er/4XZ/h4Aoent2vh4fpvVi5VJicSaWE4fdDIXjryQUwadQnxMvDcxi0QQJcWRICU7mBSX50HmUG/jEREREWng7oWbW02I6/gt3LNwc3hSfLgEDqyH/C1QtNP1dS3a4crFe8Bf0zmB14lNcslxSk7gMVBO6wdp/d2S3h9S+0FsFCSKFUWw9S1Y/wL+DS/gq6mkYT3vxwnx3N8rg3eSEpmQM5GbR17AOcPPISsxy4uIRSKWkuJIkBzyD6Ms37s4RERERJqwKbekyT7EzelPPjk7lpD/3xfJLt3iRjwu2tmJEbZBTQUc2umW1iTnuAS5PlkeEEieA4/pAyA527X46yqlB2HPCti1FHa8j929AmNrAQgdCqsGWJScxOPpaWzPHMz5oy7gOyMuYFTmqK6LVSTKKCmOBCkhSXF5nndxiIiIiDRh8ZbmP5/EUsMEs53pvs1M821ium8z/U0ggf7wCG6SkA5JmS7ZTM6CpCxITIfYRDf+SmyCW3xxgAV/ratdtn73WFPpmltXlQYeS6Cy2DXFLj0QNthUq8rz3LK/8TRF9WLiXa1yev9gwlyXSKf2cc8nIS24xCU3nUT7/XC42DUfrzzkaoArCtyXCIU7XM36gU+g7GDYaQ2vtDUulpdSUng1szeTR57NdcPPY2b/mcT4Ytr+vEV6KCXFkSCsplhJsYiIiESW0srwps2DzAFO9a3mFN9qZvnWkW4qWr+ILxayR0OfcZA5DHoNgYwhgcdBEJ/cOcEDWOuS5bKDrlVe2UG3lB6A0v1upOaSvVCyH0pzXaLdmtqqttc8Q6AftEtQ/RistVgMMbYaQxvbpYfwA2sT4lmclMii1AwGjDiDc0eex/UDTyYxNvGIryfSkykpjgQp2cGyaopFREQkwqQlGGaY9ZwTs4xTfR8zwre/xeNLbSKr/CNJHzmDydNOhD7HQM5oV9PrBWOCNbZZI1o+trYGyg5Ayb5Asryv6fLhQ0cWg/XXJ9vtmfm33Bg2x8fxUUICqxITWJWUxNhBszln+Dn8Y8gc0uI1R7RIeykpjgTqUywiIiKRprYGdrwHnzzP1ev+yxcSmv/ifo/NZpl/HCv9Y/jQP5qNdjC1xPDaOadA3yhL1mJiXZ/h9AEwsIXjqspczXJxoIa5rqa5eK9r+VdV4gYXO1wSGEW7+dr0EptEMUmU+HxUJ1kOUsG+WB97YmPZExvL5vg4dsfGYo1hSu8pnDP8HG4dNpecJM0HLdIRlBRHAvUpFhERkUhgLez9EFY9BmsXuL6tNP7AWGHjWeofzzv+ybztn8yndgANe7nOHJ7FmGhLiI9EfApkj3RLKxZvyeMLD7wP1tY3lTZYiCnDpG7AZKwjJnkrxtQ12w6fPmpSziQuH3omZw49k0Fpgzr6mYj0eEqKI4H6FIuIiIiXSvbD6idcMnxwQ5OHVCVm81TZVF6pPZ5l/nEcpvlpi3wGbpwzurOijTp3L9xMtXX9iU1sMbFp64hJW0NM8jaMabo/8eTekzlr6FmcOfRMBqQO6MpwRXocJcWRQDXFIiIi0tX8fvh0ISz/B2x+renBpdL6w/gL4ZiLiB9yArEr97B4wRpaGobKZ+CueZPD5yjuwTbuL2bFng3EZ68jNu0TYpJ2NXtsbflQqosnUVMykZ+efWH3rmkXiSBKiiNBcshAW+pTLCIiIp2pvABWPQrLH4DCbY33x6XAMRfB1Ktg6GzwBYeFuuL4IQzKTOaehZtZ2sS8xTOHZ3HjnNE9PiGu9deyOm81b+58k+c2vUbKyL1NHmetobZiKDWBRNjWZNTvW7wlT0mxSBdRUhwJEnu5IfptrRuUoeawd6MzioiISPeU+wks+SusebrpQZ+GnuQS4WMugoTUZi8ze1QOs0flsCm3hMVb8iitrCE1MZbZo3J6dBJXWVPJkn1LeHPnm7y9+20KKht/aQBgrY/a8mHUlEwMJMLpTR7XcBosEek8Soojgc/naovLDrj1sjzIaGm4QxEREZE2sBZ2LIbFd7sm0g0lZsCx18BxX2rTgFGhxvRN69FJMEBRZRFv736bN3e+yQf7PqCimRGmrT+emtIx1JQcQ03pOPC3PidzaqI+pot0Ff22RYqUnGBSXK6kWERERI6CvxY2vOCS4T0rG+/vNwmO/zJMuhziW0/QxLHWsrFwI+/ufpd3dr/D6rzV+Jvqiw1kJ2Zz2uDTGJt2Arc8Vgk27oju1dOboIt0JSXFkSKsX7EG2xIREZF2qK2BtU/DO7+B/C0NdhoYdx6c+C0YPBOMafISEq6suowl+5bw7u53eXf3uxyoONDsscMzhnP64NM5ffDpTO49GZ9x/bGfHfYBy5rog92cbj+dlUiEUVIcKcJGoNZgWyIiInIEamtgzVPwzq+hYGv4vpgEmPpZmPUtyBnlTXxRxFrL9uLtrjZ4zzuszF1Jjb/p/r0Gw5TeUzh9iEuEh2cMb/K4m+aM5poHluJvevalMJrOSqTrKSmOFJqrWERERI5UbQ2sedLVDDdMhhMyYMb1MOOrkNbXm/iixOHaw6zYv4J3dr/Du3veZVdJ89MmZSRkMHvAbE4edDKzB8wmMzGz1evPHpXDnfMmccuCNS0mxprOSsQbSoojheYqFhERkbayFtb/FxbeAfmbw/clZsAJ34CZX4WkXp6EF+mstWwp2sL7e9/ng70fsCJ3BYdrDzd7/LiscZw88GROHnQyk3ImEes78o/Qms5KJHIpKY4U6lMsIiIibbF1EbxxO+z9KHx7YgbM+qZLhhMzmjqzR8uvyGfJviX1ifDBioPNHpsUm8Ss/rM4ZdApnDTwJPqmdExNu6azEolMSoojhfoUS1scLoWDG+DAJ3BwI5TmQukBqCh0I43aWvDFuQ9DiRmQ1g8yh0LmMOg7ETKHuynAREQk+uz50CXD294O356Q7pLhE25QMhyiqraKjw58VJ8Ery9Y3+Lxw9KHcdLAkzhl0ClM7zud+Jj4TotN01mJRBYlxZFCfYqlKX4/7FoKW16Hbe+4D0S2tv3Xi0+D/lNg2GwYfgoMOh5iEzouXhER6XiH9sDCn8Hq/4Rvj0mAmV+Bk74LyVnexBZB/NbPlqItLN23tL5JdHPzBgOkx6dzQv8TOHHAicwaMIsBqQO6MFoRiSQRmxQbY64B/h1Y/bK19h9extPp1KdYQuVthg//DWsXQPHujrtuVQnseM8tb/8K4lJg9Bkw7nwYM7dDahjUJExEpINUlbl5hhffA6HJnYmBY6+GU38IGQO9i89j1lp2luxk6b6lLNu/jOX7l1NQ2fy0RzEmhim9pzBrwCxOHHAiE7InEOOL6cKIRSRSRWRSbIwZDPwJKAVSPQ6na6imWKx1/cSW/BU2v9b8cTljoe8x0OcYyBgEKX0gORNi4t0HpdoqOFwMFUVwaDcU7XBJ9r6PG3/hUl0GnzzvlthEGHsuTLkSRp0BR/hBYfGWPO5euLnJeRhnDM/iJg0eIiLSNn4/fPy4qx0u3R++b+x5cOb/g5yeOWXP/rL99Unw0n1LyS3PbfH4IWlD6pPgGf1mkBrfMz5WisiRibik2BhjgH8B+cAC4HveRtRFkrMAA1ioLILaaoiJ8zgo6TI7l8IbP4WdHzTel5QJ4y+EUXNg6EmQkt34mLawFor3wq4lrin21rehcFtwf00lrFvglowhMOPLMO0ad/9WPLF8Z4vTTCzbVsA1DyzlrnmTmX/84PbFLyLSE2x/D179kfsiM1S/STD3l67rSw+SX5HP8v3LWbp/Kcv2LWNnyc4Wj++V0Ivj+x3PCf1PYNaAWQxO0/8cEWldxCXFwI3AZ4DTAo89gy/GJR8VgVq28gLNKdgTFO2CV26GDS802GFg7Dkw/Qsw4nSI7YDBPoxxzewyLoWJl7ok+eBGd+9PnoP9a4LHHtoJr98Gi+6EKZ+FmTdA7zFNXnbxlrxW510E8Fu4ecFqBmYmqcZYRKShQ7vhlVvcNEuhUvvCnJ+4v8U9oKlvblkuHx74kJW5K1mZu5ItRVtaPD4lLoXj+h7HjH4zmNl/JqMzR+MzGlBSRI5MRCXFxpjxwF3A3dbad4wxPScpBtevuD4pzlNS3J35a2H5P1zTuKrS4HZfHEz7PMz6BmSP7NwYjIE+49xyyvcg9xPXXG/Vo8ER0KvLYcUDbhl9Fpx2CwycFnaZuxdubjUhruO3cM/CzUqKRUTq1FbD0vvgrTtdl5Y6sUlw4rdg9k2Q0D2b/Fpr2VWyqz4BXpm7kt2lLY+jkRiTyNQ+U5nZfyYz+s3gmOxj2jVnsIhIqIj5K2KMiQUeBnYCP2rnNVY2s2tce+PqUsk5wCZXVr/i7qtoFzxzvWvGHGrS5XD6jyFruDdx9T0GzroDTv8RrHkaltwLB9YF929+zS1jz3PH9JvIptySJvsQt2TptgI25ZZo8C0RkV3L4IXvQO7a8O2T5sMZP3XjRnQjfuvn06JPw5LgluYKBoj1xTI5Z3J9Ejy59+ROnSpJRHqmiEmKgZ8AxwInWWubHz+/OwvtK6oRqLunDS/Bc19z/cbr5IyFC++BISd4FlaYuCTXl/jYq2H7u7DkPtj4EhCoDt74olsmXMLa9GvadYvFW/KUFItIz1VeAAv/H6x8MHx77/Fw/h9g6CxPwupoNf4aNhRsYGXuSlbkruCjAx9x6PChFs9JiElgSu8pTO87nel9pzMpZxLJccldFLGI9FQRkRQbY2bgaod/Z61tYqShtrHWTm/m+iuBaU3tiyhhI1DnexeHdDy/330AWvzH4DYT45otn/x/kTlXsDFuQJfhp8CBDa5/8SfPBfeve5aLeZ7K2NP4bc18Ckhv86VLK2s6Pl4RkUhnLXz8H3jt1vAvv+OS4bSb4YSvR/Ugm4cOH+Ljgx+z6sAqPj74MWvy1rQ4TzBAalwqx/Y5tj4JnpA9gbgofg1EJDp5nhSHNJveBNzmcTje0lzF3VNVGSz4SvhgWumD4LIHIqd2uDV9xsH8h9xgXG/d6WqKAR9+rop9k/NjlnB3zTz+XXsW1W34s5Ka6PmfHhGRrnVwI7zwXTdPfKix58I5v4JeQ7yJq5381s/Woq0uCT7okuBth7a1el5WYlZ9Ajy973RG9xqtuYJFxHOR8Mk0Fagb1rbSzcjUyN+NMX/HDcD17a4KrMtpruLupyQXHpsP+1YFt40+Cy75W2AarijTbxJ89jHYsxIW3gFb3wIg3ZRzW9wjXBWzkDtqrmaR/9gWL6OBtkSkx6gqh3d/C4vvAX91cHv6IDj31zDuPO9iOwKlVaWsyVtTnwCvPriakqqSVs/rl9KP4/oex/S+05nWdxrD04fTzGc9ERHPREJSfBh4oJl903D9jN8DNgLtblodFVRT3L0c2g0PXQgFnwa3nfANN5hVtH8rPnA6XPMsbH6NvU98hwG1ewAY6dvHg/G/YWHtsfy05gvstr0bnTpzeJb6E4tIz7DpNXjpe1C0I7jNxLgZBk79YcSOKu23fnYU72BN3ho+PuBqgjcXbsbS8lQDsSaW8dnjmdJ7ClP6TGFq76n0S+nXRVGLiLSf50lxYFCt65vaZ4y5HZcUP2St/UdXxuWJlJAEQjXF0a1gKzx0kZvvF9yHoPN+C8d9ydu4OpIxMGYu2+e/wb8e/jnfillAunF9x+bEfMSJvnX8oeZS/ll7DjWBPzU+AzfOGe1l1CIine/QHjcHfcM5hwfPdANp9Z3gTVzNOFh+kDV5a1ibt5Y1eWtYl7eOkurWa4GzErOY0nsKU/tMZWrvqRyTfQyJsYldELGISMfyPCmWEKkh8xKX5noXhxydgq3wr3OhZJ9b98XB5f+C8Rd4G1cnOXHsAHZddDNzFpzEd2Ke4sqYt/AZS5Kp4kdxj3NJzGJ+VH0dHzOau+ZNVtNpEfHMptwSFm/Jo7SyhtTEWGaPyunYliu1NbDsb/DWL8PnoE/KhDN/BlOvBp+v4+7XDqVVpazLXxeWBB8oP9DqeT7jY3Sv0UztM9Ulwr2nMihtkJpCi0i3oKQ4kqT2CZZLlBRHpeK98O+LgwlxbCJc8SiMPsPTsDrbFccPYVDmWdyzcDhPbj+NO+P+wXifqyUf79vJMwm3kzvmKvpPOtnjSEWkJ1q8JY+7F25ucl71GcOzuGnO6KP/wm7X8sCcw2vCt0/9nEuIU7r+C8Gq2io2FW6qT37X5q1l26FtrTaDBshMyGRCzoT6muBJOZNIiUvpgqhFRLqesbb1P4zRzhizctq0adNWrlzpdSgtsxbu6B0ciONHeyFe/4CiRlk+PHguHNzg1mMT4XNPuSmNepBNuSW8v2kfo7Y+wswdfyPOXxncmT7Izck8ao53AYpIj/LE8p3csmAN/hY+7vgM3DVvMvOPH3zkN6gohDfq5hwOuUnvcXDe72HY7CO/ZjtU1VaxuWgzn+R/wvr89azPX8/Gwo1Uhw7u1Yyk2CTGZ41nUs4kJvaeyMTsiQxMHahaYBGJRu36w6Wa4khijGtCXbzbrZcegKzh3sYkbVNVDo9dHkyIfbEw/989LiEGGNM3zTVHPPlnUHidG2Rm82tuZ/FueGQeTLsWzvo5JLZ9bmMRkSO1eEteqwkxgN/CzQtWMzAzqe01xtbC6ifhtR9D2cHg9tgkOPUHMOubEBvf/uBbUFlTyabCTS4BLljPJ/mfsKVwCzW29TngY0wMozNHMyF7gkuCcyYystdIYn36SCgiPZf+Akaa1D5KiqON3w/P3eCmKQLAuCmXxsz1NKyIkDkUrnoS1j4DL30fKgJNFz98CLYsVK2xiHSquxdubjUhruO3cM/CzW1Lig9ughe/C9vfDd8+ei6c+xv3t6+DlFeXs7FwI5/kf1K/bDu0jVpb26bzB6UOqk9+J/WexLiscSTFJnVYfCIi3YGS4kijwbaiz5t3wCfPB9fP+TVMusy7eCKNMe71GH6K+xC5/n9ue32t8ecDtcYZ3sYpIt3KptySJvsQt2TptgI25ZY0P/hWdQW8+zt4748N5hweCOf8Csad7/7mtVNeRR4bCzaysXAjGws2sr5gPdsPbW9TH2CAwWmDGZ81nmOyj2F89njGZ40nMzGz3fGIiPQUSoojTehgW0qKI9/H/4H3fh9cn3kDzPyKd/FEstQ+MP9hWLcAXvxeSK3xv0Nqjbv3gGQi0nUWb2nf1IaLt+Q1nRRvfgNe+j8o3B7cZmLghK/Babcc0ZzD1f5qth3axsaCjWwq3FSfCBdUti2JNxiGpg/lmOxjXAKcNZ5x2eNIj1eXFBGR9lBSHGnSQia5L219igTx0P418L+bguujz4K5v/QunmhgDEy8FIbV1RoH5vAs3gOPXOr6Gs/9BSR04BQpItIjlVa23r+2TecV74VXboFPngvfPuh4N+dwv0ktXq+osqi+5ndjoUuCPy36tE0DYIGbCmlExoj65PeY7GMYmzVWI0GLiHQgJcWRRjXF0aGiCJ64BmoCIyv3HgeXPgC+GE/Dihqpvd1AZOuedQNxlee77R8+BFsXwcX3dtmIrSLSPaUmtu8jTv15tTWw/O/w5i+gqiR4QGIvOPP/wbGfD5tzuMZfw87ina7mNyQJbsscwHWSYpMYkzmGsZljGZs11pWzxqoPsIhIJ1NSHGnC+hSrpjgi+f3w3NegcJtbj091zYI1kvKRMQYmzoNhJ4fXGhftgAfPgxO+DnNugzh9GBSRI9feeYdnj8qB3SvhhW/D/tXhO6d8Fv+Z/489/iq27H6bLUVb2Fy0mU+LPmXboW1trv0FGJAygDFZwQR4bOZYBqUNwmd8rZ8sIiIdSklxpNFAW5Fv6b2w8aXg+kV/gd5jvIsn2tXVGq95ytUaVx4CLCz5C2x5Ay65DwZO8zpKEYkyY/qmMWN41hENtnX60HjGLP8prPgnoXMOF6X15enRs3jDV8TW5y+goqaizddMiElgVK9RwZrfzLGMyRqj/r8iIhFESXGkCWs+rZriiLNvNbxxe3D9hG/AhIu9iqb7MAYmz4dhJ8Hz34RPF7rteRvhH2fAKd+DU74PMXHexikiUeWmOaO55oGlrU7LZGJKuCT+NX5W+CrkltZvrzSGv/VK58GMeGoKP2z1fn2T+zI6c3RY7e+Q9CGaA1hEJMLpr3SkSWnQp9jao5reQTpQVTk8cz3UVrn1/lPhjNu9jKj7SR8AVz8DKx+EV38M1WVga+HtX8HGl938z32P8TpKEYkSs0flcOe8SdyyYA1+68fEFeGLP4gv4UD94wizi9uK9nJC5WGoCp77blIiv8zOYndc449KWYlZjO41mlGZoxjZaySje41mRK8Rqv0VEYlSSoojTXwyJKTD4WI3B2JFISRneR2VALx+m6u5BIhLhkv/AbHx3sbUHRkDx30RRpwGz30ddr7vtu9fDfefCp+5FWZ9U4OaiUiTqmqr2FG8g62HtrL10Fa2VWxj3PTN7C7dgTXBPr+Jfj/XHyrmi0XFhP4lz42J4a7sTN5ITiItIZ1pvUYzstdIRvUaxehMV85K1P9lEZHuRElxJErt45JicE2olRR779M3Yfk/gutn3wk5o72LpyfIGg5feAGW/BUW3gG1h10t/es/cbXGF/8VskZ4HaWIeKS4qphth7axtWgr2w5tc+VDW9lduhu/9Tc+IaTR1anl5dycX8igmtr6bX5gyZCpbJt2FZf3nsTNvUbSJ7kPRq21RES6PSXFkSi1L+RvceXS/dBnnLfx9HSHS+C/NwbXx53v5tOVzueLgRO/BaPOhGe/CvtWue07P4B7Z8NZd8Bx16mLgUg3VVVbxa6SXWwv3s6O4h3sKN7B9kPb2Vmyk7yKvCO+3jG+FG7OL+TYovBz7cDj8J3/e07sP4UTOyp4ERGJGkqKI5EG24osr/8UDu1y5aRMOP8PSsK6Wp9xcP0b8O7v4J3fgL8Gqsvhxf+DDS/ChX+GjIFeRyki7VDrr2Vf2T6X8IYkvzuKd7C3dC+WVkbJasBgGJA6gOEZwxmRMYLhGcMZmTqIcetfI+mDvwTnlwf3N/2M2zEN5hwWEZGeRUlxJNK0TJFj2zuw4oHg+jm/Dv/SQrpOTBycdjOMmQvP3gAHN7jtn74Jf50F5/7GjWCtLyxEIo61lryKvLCEty4B3lWy64jm960T54tjaPpQRmSMYESvEQxPH86IXiMYmj6UpNiQ+c23LISnvw4Fn4ZfYNrnYc7tkJJ9dE9ORESinpLiSJTaYARq8UZ1JfzvpuD62HNh0uXexSPOgGPhK2/DWz+H9/8MWDh8CJ79Cmz4H5z/R0jJ8TpKkR7Hb/0cKD/ArpJdYcvO4p3sKN5BeU35EV+zrtZ3aPrQRkv/lP4tT3V0aA+8+iP45Lnw7f0mw3m/h8HHH3E8IiLSPSkpjkRhNcVqPu2Z934PBVtdOSHDfYhSLWRkiEuEs37uvqh47mtQuN1tX/8/2PEBXHA3jD/f0xBFuqOq2ip2l+5md8nuRsnvnpI9VPmrWr9IE3KSchiSNoRhGcOCiW/aUAanDyYhJuHILlZTBUvvg0V3uWnd6iRkuNHrj79Oo9eLiEgYJcWRKLVfsKyaYm/kbYH3/hBcP+OnkN7fu3ikaUNPhBsWu+myVvzTbSvPgyc+B1M+C2ffBUm9PA1RJNqUVJWEJbt1CfDOkp3kluUecR/fOmlxaS7ZzXAJb2g5NT61Y4Lf9Bq8ektwsMo6k690A/Op+4uIiDRBSXEk0kBb3rIWXvyum/4HYOBxMP2L3sYkzUtIdYOfjTsPnv8mlOxz2z9+3PUJv+jPMPIz3sYoEkEO1x5mb+le9pbuZU/pHvaU7qkv7yrZRdHhonZfOzMhk8FpgxmUNojBaYPrl6HpQ8lKzOq86Y0ObnJNpbe8Hr6993g477cw7KTOua+IiHQLSoojkQba8tbaZ2Db265sfHD+7zUqaTQYdQZ8/QN4+Yew+gm3rXgPPHwJHH89nPkziE/xNkaRLlBdW83+sv3sLt3dZOJ7sOJgu6/tMz76JfdrMvEdnDa442p826qiyI1Iv/Q+Nyp9nYR0OPWHMPOrbpA+ERGRFigpjkQpOS4Zs34oz4faav1T7ypVZfDabcH1mTdA/ynexSNHJikT5t3v5pJ+4dvu9wdg+T/cCLSX3AdDTvA0RJGjVeOvIbc8lz0lexolvHtK93Cg/EC7mzgDJMQkMCh1UJOJ78DUgcRFwv8jfy189DAsvMN1mahnYPq1cPqtkNrbs/BERCS6KCmORL4YSM6BskDT6bKDkD7A25h6isV3Q8leV07pDafd4m080j7HXOiS3/99Gza+6LYVboN/ng2zb4TTfuQG6xKJQOXV5ewv38/+0v3sK9vH/vL97C3dy76yfewp2UNueS61trbd16+r7R2YNpABKQMYmDaQgamuPDhtML2Te+MzEdw6Zuvb8NqtsH91+PYhJ8I5d+mLTBEROWJKiiNVat9gUlyaq6S4KxTtdElxnTk/hcR07+KRo5PaB658FD7+D7z8AzhcDFj3M970Glz8Vxg4zesopYfxWz95FXnsK9vnEt5A4ruvbB/7y1z5aPr0gpvGqE9yHwamBpLd1AFh5b4pfYnzRUBt75HK/QRe/0njfsPpg9wgWhMu0QwBIiLSLkqKI1VqH6jrTqzBtrrG6z+BmkpX7j8Vpn7O03CkAxgDUz8Lw0+G578BWxe57QfXwz/muObxp/8IEtI8DVO6j/Lq8vokd1/ZPvaVBpPdfWX7yC3PpSa072s75STl1Ce5g1IHMSB1QH25X0o/4mPiO+DZRIjivfDWL2HVo65bUZ3YJDjp23DijRCf7Fl4IiIS/ZQUR6rQwbZK9nsXR0+xcwmseza4fvZdGlyrO8kYBFc/CysecF9+VJe7D9dL/gqf/BfO/Q2MO7fLw9qUW8LiLXmUVtaQmhjL7FE5jOmrBD0SWWsprS7lQPkBcstyyS0PLnXb9pXto7iq+KjvFWti6ZvSl/4p/emf0p9+Kf3on9o/rMlzYuyRNf+PyvdaZTG8fw+8/2eoqQjZYdyXlqf/CDIGehaeiIh0H0qKI1VayFzFdVPMSOewNnxwrQnzYOgs7+KRzuHzwYwvw6g58MJ3YetbbnvxbvjPZ2H8BXDOr7ukq8LiLXncvXAzy7YVNNo3Y3gWN80ZzexROZ0ehzh+66ewstAlt+W5zSa95TXlHXK/Xgm9gsluXeKbGixnJ2YT44vpkHtF5XutthpWPgiL7mowiBZulPkz/h/0m+hJaCIi0j0Za9s/QmW0MMasnDZt2rSVK1d6HUrbLfs7vPQ9V572ebjwT97G052t/x88cbUrx8TDN5dD5jBPQ5JOZi2seQpeuSX8Q3d8Gsz5CRx/nRvwrhM8sXwntyxYg7+FP70+A3fNm8z84wd3Sgw9SY2/hryKPPaX7Q9LeuvLgaS32l/dIfeL88U1quGtK/dL6Ue/5H4kx3VNU9+oe6/V1sCaJ10yXLQjfF+/SXDmHTDydG9iExGRaNGuwSVUUxyp0kOahBXv9S6O7q62Gt64Pbh+/PVKiHsCY2DyfFfr9Ppt8NEjbntVCbz8fVj9Hzj/j9B/cofedvGWvFaTFAC/hZsXrGZgZlLk1eJFiFp/LQWVBRyoOEBeeV6TjwfLD5JfmY8/tB/qUUiMSaRvSl/6JPehb3Jf+iYHyimu3C+lH1mJWRExcnNUvdf8fli3wCXD+ZvD96UPgjm3waT56tIiIiKdRklxpAptwlms5tOd5sN/Q/4WV05Ih5O/52080rWSs+Civ8CUz7rpm+o+kO9ZCfefCtO/CJ+51R3XAe5euLnVJKWO38I9Czf3uKS4xl9DQWUBB8sPcrDiIAfKD5BXkdfosSOTXYC0+LT6RLcuya1PfgPr6fHpmCgZ3Tgq3mvWwoYX3SBaB9aF70vKcoNozfiqpk8TEZFOp6Q4UoXVFO/xLo7urKoc3v5VcP2k70BKtnfxiHeGnQRfWwzv/QHe/R3UVrmBuFY84GqwPnMbTP/CUTWp3pRb0mS/zpYs3VbAptySyB8QqQ2qa6vJr8wnryKvPuE9WHEwWA485lfkY+nYbj3ZidlhiW6/lH6Nanu7qklzV4j495q1sOUNePPnsG9V+L6EDDjxm25keE2JJyIiXURJcaRKznb9W2uroLIIqsogPsXrqLqXZfe7OaAB0vrDCV/zNh7xVmwCnHYzTLzUzWv86Ztue0UhvPhdWPkvOOc37R6EbfGWvNYPaua8SE2K62p18yvy62tv8yryyK/Id9sq8+r3dcSozA1lJmSSk5xDn6Q+9E7uTe+k3o0fk3oTFxOFc/IehYh9r/n9sPFF98XT3o/C98WnukT4xG9CUmbnxSAiItIEJcWRyudziVrdYCPF+yBnlLcxdSeVxbD4j8H1U38AcUmehSMRJGc0XL3ANet89RYo2um2718D/zobjrkIzrgdskYc0WVLK9s3N217z2uvWn8thYcL6xPb0EQ3rzIvLOktOlzU4bW6AFmJWeQk5YQltr2Te9MnqU99EpyTlNPjkt22irj3Wm01rHnatcTI2xi+LzbRjQo/+9uQ0rO6CoiISORQUhzJ0geGJMV7lBR3pCX3uhpAgF5DYerV3sYjkcUYGH++m77p/T/Bu78PzpP6yfOw4SX3Qf6U77e5v3FqYvv+3Lb3vFDVtdUUVBZQUFlAYWUh+ZX5roa3Mj9Yq1vhEt7Cw4Ud2le3js/4yErMIjsxu9la3T7JfchOzFaye5S8fK+Fqa5wg9gtvgcO7QzfF5PguiSc/N3wKQhFREQ8oKQ4koUNtqURqDtMeQF88Ofg+mk3Q2y8d/FI5IpLcq0IplwJr//U9S8G8FfDkr/CqkddYjzjK675dQvaO4hRU+fV+GsoOlwUlujWNWMuPFxIQUVge6BcUl3Srnu3xmDITMysr9nNTsomJzHwmJRDdmJ2fblXQq8Om3tXWtaR77V2qTwEK/4JH/wFyg6G74tPc1OenfB1SOvbMfcTERE5SkqKI1l6/2BZg211nPf/BIcD/RuzR7upPkRa0msIXP4v90H+tVth1xK3vfKQW19yH5z6fZj6OWimlnNM3zRmDM9qZgAkPyamAhNTioktq38clFPLk9s+omB9QVgCXHS4qNOeKkBGQgbZieGJbV1yW7ctJymHzMRMYn3e/RvZlFvC4i15lFbWkJoYy+xRORHb/7ortfxea9rM4VlH/9rlfwpL74NVj0FVafi+5Gw3bsPxX4akXkd3HxERkQ6mpDiSaa7ijlde4AbYqnP6LRCjXwNpo8HHw5degfX/gzd+CgVb3fbi3fC/m+C9P8Jpt1Ax/jyKqkooPOwS2KLKIgoPFzJi9F5WV2yCmHKX+MaUBZLgMoxp3Dc3D3hiY6PNR8xnfGQmZJKVlEVWQhZZiVlkJmYGa3dDk98oaL68eEsedy/c3GTSN2N4FjfNGd3jprJq6KY5o7nmgaVtmpbJZ+DGOaPbdyNr3aB0S++Dza813p8+EE68EaZdo8EiRUQkYikbiGShzadLNFdxh1hyb7AGo/c4OOYSb+ORiFdZU+kS28NF9bW0Rb4yik/6EsM3v8WsLe+TVh3ob1y4DZ79CnteiOPezAxeT07CNpjXNq4DBtY1GHol9KpvulyX5GYnZodtq1vSE9LxGd/R3zgCPLF8J7csWNNssrdsWwHXPLCUu+ZNZv7xg7s2uAgye1QOd86b1OJrBS4hvmve5CP/EqGqHFb/B5b+DQ5uaLy/9ziY9Q2YfKW6p4iISMRTUhzJNFdxx6oocrUZdU75vhvlW3qMqtqqYGJ72NXe1tXiFlUWNU5+DxdRUTfAVjOSBmRzVXEJXzxUQobfDVA1qrqa3x3IY2tcLP/ISOfl1BRqGiTHDdnaRGxNKilxvRib05/ROf3qE9yGyW5GQoanzZa9snhLXqtJHoDfws0LVjMwM6lH1xhfcfwQBmUmc8/CzSxtolZ95vAsbjzSWvWDm+DDh9wAWpVFjfePngsn3AAjTncD1omIiESBnvepKppooK2OtfRv4X2JJ6iWOFodrj3MocOHgkvVIYoPF9eXDx0+RNHhIretKnhceU15h8dS4fPxQK8MnkxL45riYj5/qIQU67K2EdU1/DKvgO+VVrFkxAnsHHkyacm9XS1vQial5Yls3OuntjqZjKQk9Yltxd0LN7epOTC4xPiehZt7dFIMrsZ49qico+t/XVXuRl3/8CHY+UHj/fGprj/9zK9C9siOfQIiIiJdICKSYmNMNnAJcB4wCRgIVAFrgH8B/7K2E+YIiXSpfcHEgK11I3jWHG51hFtpRmUxLPlLcP2U74NGwvWUtZbK2sr6hLW4qpiiw0UtJrp1S2VtZZfFGeuLJTMhk16JLpGta7bcK6GXW+q2Bx5NbS12+T8xy/9R/yVMVmUp537yBuxc46Zymn42pGQDcFY7u3L2NJtyS45o4CiApdsK2JRboi8acINvHfHrsO9jWPkQrHkq+IViqMxhMOOrcOznIDGjQ+IUERHxQkQkxcDlwL3APuAtYCfQF5gH/AM4xxhzubW2jXUE3YQvxs3fWNd0umSf+xAiR27FA26kYICsETDxUm/j6UZq/bWUVpdSXFVMcVUxJVUlYYluXbku4Q3dVuWv6tJYY00svRJ7NU5sG6zXlTMTM0mOTcYcaTPQM34Ks2+C5X+HD/4KFYFkrjQX3vw5vPNbN83TzK9Bn3Ed/0S7ocVb8tp9npLiI1CWB+uehY8edklxQ75YGHM2TLvWzeOtLxdFRKQbiJSkeBNwIfBiaI2wMeZHwDLgUlyC/Iw34XkofUAwKS7eq6S4PWoOuwG26pz0XY043UBlTWV9Qhua2IauN3o87B47aw7clsT6YsmIzyAjIYNeCb1IT0ivX89IyKgvpyek0yuhlyvHp5Mal3rkCW57JfVyLRJO+LqrbXv/nuCAeTWVsPJBt4yc45qdjjpDCUYLSitruvS8HqWyGDa8CGufhk/fcq2TGsoaCdM+D1M+q/mFRUSk24mIzMBa+2Yz2/cbY+4DfgGcRk9NiuuoX3H7rH7C1dABpfG9eaZsBrO6WZPK0NraphLXulrc5vZ3dY1tnXhffDCpDUlm65b0+GBSG7o/KTap65LboxWfArO+DsdfD+sWwAd/gf2rg/s/XeiWjMEu6Tj26vDfewEgNbF9/67ae163V10JW153TaM3veq+qGkoJgGOuQimXwtDZ2vgLBER6bai4dNCdeCxZ37drxGoj8rizQcY9uKvqHsV7y47k7+/uAVe3BJR85lW1VZRUlVCaXUppVWllFSXuMeqkvrtoY8NE9vS6lIs3vUuSItLIy0+jfSEdNLi0xrX1MaHJ7p15cSYxOhJbo9WbLxrMj35CtjxPiz5q6udq/u5HdoFb/0CFt3lmqdOv9bVIqtVA0C7f08j4fc7YlSVuTmFN7wEG15oup8wwOATYNJlbknqgDnEREREIlxEf9oyxsQCnw+svtKG41c2syt6O+2l9Q+WVVN8RJ5YvpM3n/snf4vbDUCxTeLx2s/U7++o+Uyra6uDSWx1IImtKm0yyQ1NausT3apSz2pq68T6YkmPT69f0hLSwtfj04KPCcH1uibJMWr223bGwLDZbinY5vq7r3oMyvPdflsLG190S0pvmHgZTLkC+k/t0TV1Y/qmMWN41hENtjVzeFa3ahHSLiW5sOkV2PgSbF3UdI0wQN9JMOlSN95CryFdGqKIiIjXIjopBu4CJgIvWWtf9ToYT6j5dLu4+UxX83Tc/+q3PVp7BqUkhx3ntzXc/PwHxCcWMHpArEtcQ2tqm0pmQ9ZLq0s5XHu4q59ek1LjUsOT12aS2PT4dLctLrivR9XYRpKs4XDWz+Ezt8H6/7k+xtvfDe4vOwhL73VLzliYPB8mznODxfVAN80ZzTUPLG3TtEw+AzfO6YFDe1sLBze6JHjjS7B7BTTXiiRzGEy63H3xogHfRESkBzOROqCzMeZG4G5gAzDbWntkc3GEX2vltGnTpq1c2VxFcgTb8QH862xXHngcfHmht/FEgFp/LeU15ZRVl1FWXUZpdSllVYHHwLYH3l9P/4JNPFb+GgBVGM7ImUFeHBjfYfAdxvgOY3yR0So/1sSSGp9an9iGleNSSY1PJS3ObW+Y4NYdH+uL9O+4pE3yNrv5YFc/BaX7mz6m7yQ45kIYfyH0HtujapCfWL6TWxasaTEx9hmOugVIVCnJhW1vu0Gyti6Ckha+QO09HsadC+POgwHTetR7R0REeoR2/WOLyE/Rxphv4BLiT4A5R5MQR71uUlNcNydtS4lsaXUp5dXl9dtKq0opqylrdFx5TXnrN4yDn9oD9av/TU2mMG0fndHIN8bEhCWxdYlsUwltWHIbF0x+o2rgKOlcOaNd7fEZ/88lOqufhE/+C9VlwWNy17jlrV9A9mgYfz6MPgsGzej2fZCvOH4IgzKTuWfhZpY20ZR65vAsboyQsQI6TVWZ65e+dZFLhA+sa/5Y44MhJ7pEeOw5PbaVgYiISEsirqbYGPNt4A/AWlxCfKDlM9p0zeitKa6pgp/3dmXjg1sPdtmH3mp/NeXV5ZRXl9cno3WPjbZVl1NeU95sIltWXUZtU9N8dJKRVVU8t8fVsvmBiwb2Z3t8XKPjrPVBbSLWn0jf1AyGZmY3SljT49OV0Iq3qsrc4Ehrn3EDJTXXZD8xA0acDqPPdFM8pfXr2ji72KbcEhZvyaO0sobUxFhmj8rpnn2IS3Jh1xLYudQ97vsY/C20cknIgBGnwthzYcxcSM7qulhFRES8Ff01xcaYH+L6Ea8CzrTW5nkbUQSIjYeUPlB2AKzfNafMGNTosNCa2IrqCspqysIS1+aS2IbbK2oq6pPYan91EwFFhpS4lPolNS417HFLbjXz179ef+wbZhSf5F4J/kRsbQLWn+DK/gSwsdT97lxy5hi+1RP7IErki0+ByZe75XCJm0Jn/X9h8+tQHdJyovIQfPKcW8A1lR12Egw/GYaeBCnZXkTfacb0Tet+SXBtDeRthJ1LYNdS91i0o+VzfHEweIb7QmTk6W5Qtm7eYkBERKQjRcx/TWPMbcDPgJXAWT2lyXStv5YdJTuarpENJK4Xx8VS14j6jwu/y+qU1EYJb3lNOX7r9/S5tCYhJqFRIhu2Hp9CSmwKqfHBJDc5Ltk1QQ45PjkuGZ/xNXufJxYu4YLqv9d/T3Rv5TXU2taTXc1nKlEhIS04XU5Vuas53vwabHmj8bRtB9e7Zfnf3XqfCTB0Fgw63i1ZI9Sn1Es1h+HAJ67md99q95i7tvkRokP1Hu8S4BGnw9ATISG18+MVERHppiIiCzDGXItLiGuBd4Ebm2iOut1a+2AXh9bpymrKuOi5i1o8ZkR1UX1SnLt3BcvTUjo/MMBnfKTEuiQ0OS45vByXQnJs8LFue8Na29ByXEzj5sud4cziBcQZ11R7qX8cH7UhIQbNZypRKD7Z9Scef74bdfjAJ672eMsbroaxYWuPA+vcsvwfbj0p0yXHA4+DfpPckjFIiXJH8/vh0E44uMnVAh/Y4BLgg+tbbgZdJzbRDYo1ZKabQ3jwDDWJFhER6UARkRQDwwOPMcC3mznmbeDBrgimKyXHJrd6zJ7Y4I9pUE3zH6ASYhLCEtS6JDY0cQ1LYuuS2maOSYhJiL6+sodLyFr/WP3q32rOb9Npms9Uop4x0HeCW076tuuHvGuZm+Jp+3uwZ2XjBKyi0NUyb34tuC2xVzBB7j0Ocsa4pZs1ve4UFUVQtBMKtkLeJjc1Ut5GyNsCNRVtv07aABg0HQYHkuD+U1xXGhEREekUEZEUW2tvB273OAxPxPpiGZ05mlgTG0xQG9TIjt/xEXz0FACX9J7O9M/8MDzhjUsmKTaJOF/X1MRGtFWPQVUJAJ/6+/OWf2qrp/TY+Uyle4tPcc1rR57u1g+Xwu5lbt7a3cvdUlHY+LzKokAi/W749qQslxxnj4JegyFjMPQa4srpA6GLWoJ4xu+HigIo2e+aqRfthMLtrr9v4Q73WHnoyK+bOdwlvf0nu8d+UyC1d4eHLyIiIs2LiKS4p1tw4YKWD0h9oz4pHlBdzYD+J3RBVFHI74elf6tfLZr0JcyHPloaYL1uPlM1nZZuLyEVRn7GLeCaWxdsdcnxvo9h/xrYv7r5xK6iwI18vGtJ433G52o36xLklN6QkhNYerslOds9JqRFRvNsa92gZZVF7suB+qUIyg665Lc0F0r2udGfS3MbN0c/Esk5bk7pnDHuse9EVxuf1KuDnpCIiIi0l5LiaNBrWLBc2MoopD3Zlteh4FNXTshg+oVf5+FjK3v2fKYizTEGske6ZcqVbpu1cGhXIEFe65oA522C/C3ho1w3ZP1QvNstrfHFuQQ9Ps3VZiekQnxqoJwGcckQE+9GT/bFuuN9sSHrse5+/lqwte7LMFvrmobXbauudPFWl0N1hWtKXl0R3FZZ7BLgjp4mLjbR1Z5nDgs2O69LgtUHWEREJGIpKY4GoVMwFe9xU3Zouo3GltwbLE+7BhJSmT0qldmjcnrOfKYiR8OYQJPoITDuvOB2v9/97cnbGGgyvMslz0W7XDPi0v1tv4e/OlgrG20S0t3cz2n9Aq/TMMgcCr2GusfUvpFRCy4iIiJHRJlVNIhLhLT+rhmfrXW1MZnDvI4qshzYAFvfcmXjgxlfCdvdLeczFekqPp9rGt1rcNP7aw7Dod0uUS7eC2V5UJ4HZfmuKXJ5nnssy4fqsq6NvSVxKW4E7qReDR6z3N/ctL6Q2i/4GN/6wIgiIiISfZQUR4teQ1xSDK5mRklxuKX3Bctjz3W1NiLSNWITgk2xW1NdCVWlbjlc2kS5zDWFrq0ONon2V4dsq3VffPl8YGLAFxN4jA1ui010CWxc3ZLkmmfHJblEOCHVJb+xCZ3/2oiIiEjEU1IcLXoNhV1LXblwR3ASK4HyAvj4P8H1E77mXSwi0rK4RLekqC+/iIiIRAaf1wFIG/UaEiwXabCtMB/+OzgHaN9JMHS2t/GIiIiIiEjUUFIcLUKbAxft9C6OSFNbA8v/EVw/4QYNdCMiIiIiIm2mpDha9ApJijUtU9DGF93gPuDmAZ14mbfxiIiIiIhIVFFSHC3Cmk+rprjekpABto77ouurKCIiIiIi0kZKiqNFxiA34iq4UahrDnsbTyTYtxp2vu/Kvlg47jpv4xERERERkaijpDhaxMRB+sDAioWiXZ6GExFC+xIfczGk9/csFBERERERiU5KiqNJaL/inj4CdUURrHkquD7jy56FIiIiIiIi0UtJcTTJVFJc7+P/QHW5K/edCINnehuPiIiIiIhEJSXF0USDbTnWwooHguvHX6dpmEREREREpF2UFEcTTcvkbH8X8ja5cnwaTJrvbTwiIiIiIhK1lBRHk7Ca4h6cFIcOsDXlSkhI9S4WERERERGJakqKo0nW8GC5YKt3cXipeB+sfyG4frymYRIRERERkfZTUhxN0vpDXIorVxRCWb638Xjhw4fA1rry0JOgz3hv4xERERERkaimpDiaGAPZI4Pr+Vu8i8ULtdWw8sHg+vFf8iwUERERERHpHpQUR5vsUcFy/mbv4vDCxpehZJ8rp/SBcRd4G4+IiIiIiES9WK8DkLbZlFvC4i15TCjJZkbdxp5WUxw6wNb0ayE23rtYRERERESkW1BSHOEWb8nj7oWbWbatAICLfHHMCOSCS5cvpWZYHrNH5XgYYRfJ2wzb3nZl44PpX/A0HBERERER6R7UfDqCPbF8J9c8sLQ+IQbYagfUlzMrdnDNA0t5cvkuL8LrWiv+GSyPOQcyBnkXi4iIiIiIdBtKiiPU4i153LJgDX4bvn2b7VdfHmpywfq5ecFqFm/J6+IIu1BVGXz0aHBd0zCJiIiIiEgHUVIcoe5euLlRQgxQSjIHbC8AEkwNA81B/BbuWdiNB91a+wwcPuTKmcNhxOnexiMiIiIiIt2GkuIItCm3JKzJdEOhtcUjzH4Alm4rYFNuSafH1uWsDR9g6/jrwKe3rYiIiIiIdAxlFxGotabQn/r715dHmL1tPi8q7fkQ9n3syrGJMPVz3sYjIiIiIiLdipLiCFRaWdPi/m02mBQPD9QUt+W8qBRaSzzxUkjO8i4WERERERHpdpQUR6DUxJZnytpqm64pbu28qFNeAOsWBNeP0wBbIiIiIiLSsZQUR6DW5h0Oqyn2BWuKu918xasehZpKV+4/FQZO8zQcERERERHpfpQUR6AxfdOYMbz5ZsI7bR9qrPvRDTT5JFHJzOFZjOmb1lUhdj6/H5Y/EFw//jowxrt4RERERESkW1JSHKFumjMaXzM5YA2x7LR96tdH+PZz45zRXRRZF9n6FhRuc+WEDJh4mbfxiIiIiIhIt6SkOELNHpXDnfMmNZsYh/Yr/vHM+O7XdDq0lnjqVRCf7F0sIiIiIiLSbSkpjmBXHD+Eh6+bycwmmlKH9is+sVdhV4bV+Q7thk0vB9eP1wBbIiIiIiLSObrZcMXdz+xROcwelcOm3BIWb8mjtLKG1MRYzqk6Dd5+yR10YL2nMXa4lQ+B9bvy8FMgp5s1DRcRERERkYihpDhKjOmbFj6Q1u7j4O1AOXetJzF1itpq+PCh4Prx13sXi4iIiIiIdHtqPh2t+owDAh2O87dAdYWn4XSYDS9Aaa4rp/aDsed6G4+IiIiIiHRrSoqjVXwKZI1wZeuHgxu8jaejhA6wNf0L8P/bu/dwq8o6gePfHxwQMEHQvIGF4gULLQHBtFLRtEzLazVT2phaTj2mZY/2NKXTNI02jUl2c/IyZtg8ZTebMkUL864J2HhJUAhvIAIqoiAivPPHWmf24XCOwjlr77XPXt/P86xnve9ee7/rt5/nZS9+533Xu/oPKC0USZIkSa2vqZLiiBgVEVdExMKIWB0RCyJiakQMLzu2prTtW2vlxQ+WF0dRlsyBBbdm5egPEz5ebjySJEmSWl7TJMURMQaYCZwE3ANcBMwHzgDujIitSgyvOW23Z63cCklxx1HisYfD0B3Ki0WSJElSJTRNUgx8H9gG+GxK6aiU0hdTSlPIkuPdga+XGl0z6jhS/PT95cVRhFdegr/8d60+0ccwSZIkSaq/pkiKI2Jn4FBgAfC9TofPA14CToiIzRscWnPrPH06pfJi6a37r4HVL2TlEWNgpwPKjUeSJElSJTRFUgxMyffTU2p/QG0mpbQCuB0YAuzb6MCa2rA3wcD8MU2rnoUVT5cbT0+lBH++rFbf52To1yxdU5IkSVIra5bnFO+e7+d2c/wRspHk3YA/dNdIRMzs5tDYnofWxPr1y0aLn7grqy9+EIZuX25MPfHkvbXp322D4G1/V248kiRJkiqjWYbjhuX75d0cb399y/qH0sesN4X6gfLi6I17OyywNe44GDKivFgkSZIkVUqzjBS/nsj3r3nTbEppQpcfzkaQxxcdVFPo60nxymfhgV/W6vt8orxYJEmSJFVOs4wUt48ED+vm+NBO71O7bcfVyn3xsUyzp8Ha1Vl5h71hZJd/15AkSZKkumiWpHhOvt+tm+O75vvu7jmurm3fUisvnQuvri4vlk21bh3ce0Wt7mOYJEmSJDVYsyTFM/L9oRGxXkwRsQWwP7AKuKvRgTW9zbaA4aOz8rpXYcmc13x7U5n/R3jub1l50DAYd2y58UiSJEmqnKZIilNK84DpwGjgM50OfxXYHLgqpfRSg0PrG7bbs1ZeOKu8ODbVPZfWym//KAwcUl4skiRJkiqpKZLi3KeBZ4CLI+LXEXF+RPwR+BzZtOl/KjW6ZjZqn1r5iT+XF8emWDYP5l5fqzt1WpIkSVIJmiYpzkeLJwJXApOBs4AxwMXAO1JKy8qLrsl1TIqf7CNJ8d2X1Mq7vRe23qW8WCRJkiRVVlM9kiml9ARwUtlx9Dnbvx36tWX3FC+dA6ueg8HDy46qe6ueh9lX1+r7/mNpoUiSJEmqtqYZKVYvDByy/qOZnppZXiwbY/Y0WJPfHr7NW2CnA8qNR5IkSVJlmRS3ih0n1crNfF/x2lfh7v+s1SefBhHlxSNJkiSp0kyKW8V69xXfU14cr2fOdbD88aw8eATs9aFy45EkSZJUaSbFrWK9pHgmrFtXXiyv5a4f1MoTPwEDBpcXiyRJkqTKMyluFcNHw5Cts/Lq5bB0bqnhdGnhffD4HVm5Xxvsc0qp4UiSJEmSSXGriFj/vuJmfDRTx8cwvfVoGLp9ebFIkiRJEibFrWXUxFq52e4rXrEY7v95rT7ZxzBJkiRJKp9JcSsZ1cQrUN97Oaxbk5V3nAyjJpQbjyRJkiRhUtxaRo6H6J+Vl/wVXlpabjzt1qyCP19eq+/rKLEkSZKk5mBS3EoGbr7+KtTzZpQXS0ezp8HKPEEfOgrGHlluPJIkSZKUMyluNbscXCvP+0N5cbRb+yrccXGtvt/p0L+tvHgkSZIkqQOT4lYzZkqtPO+PkFJ5sQA8+Et4/vGsPHgEjD+h3HgkSZIkqQOT4lazw94weHhWfnExLH6wvFhSgtsuqtUnn5ZN8ZYkSZKkJmFS3Gr69YedD6zVy5xC/ch0eOahrDxgc5h0anmxSJIkSVIXTIpb0ZgO9xU/WlJSnBLc8s1afeJJMGREObFIkiRJUjdMiltRx/uKH78TXlnZ+BgevQmezJ+V3H8g7PvpxscgSZIkSa/DpLgVDRsJbxyblde+Ao/d3tjzpwQz/q1Wn/APWUySJEmS1GRMilvVelOob2rsuefeAAtnZeX+m8E7P9/Y80uSJEnSRjIpblUdn1f80LWwbm1jzpsS3Hx+rT7xJBi6fWPOLUmSJEmbyKS4Ve30bhiydVZesQgW3NaY8z78O1h0X1ZuGwTv/FxjzitJkiRJPWBS3Kr6D4Bxx9Tq//uz+p9z7Rq46bxafeLJsMV29T+vJEmSJPWQSXEr2+vDtfJD18KaVfU9371XwLJHs/Jmw+BdZ9X3fJIkSZLUSybFrWzkBBixc1Z+ZQXM+X39zrXqebj5glr93WfB5lvV73ySJEmSVACT4lYWsf5o8f3X1O9ct14Iq57Nylu+CSZ9qn7nkiRJkqSCmBS3uj2Pr5UfmQ4vLSv+HEsfhbsvqdUPPg8GDCr+PJIkSZJUMJPiVrfVGBi1T1Ze9yrcN63Y9tetg/85A9a+ktVHToRxxxZ7DkmSJEmqE5PiKtj7hFr5ju8Wu+DW7B/DY/njnqI/HHFRNm1bkiRJkvoAk+IqeNtHYOjIrPzSMzDzR8W0u2Ix3PiVWn2/02H7vYppW5IkSZIawKS4Cto2g/3PrNVvnwprXu5dmynB7z4PLy/P6sN3ggO/2Ls2JUmSJKnBTIqrYvyJ8IbtsvKKRb2/t/iu78PDv63Vj5wKAwb3rk1JkiRJajCT4qoYMAj2/2ytfutFsPrFnrX1+F1w47m1+qRPwc4H9io8SZIkSSqDSXGVTDgJhmydlV94Eq4/Z9PbePEZuOakbCVryFabPvRfi4tRkiRJkhrIpLhKBg6Bw75eq8+eBvf/fOM//+ISuOqDsGJhVh88HI6/EtoGFhqmJEmSJDWKSXHV7PVh2PNDtfpvPwfPLXj9z724BH50JDzzUFaPfnDMZbDljnUJU5IkSZIawaS4aiLg/RfC8NFZffULcOUR8NSs7j/z1Ez4r/fBkr/mbfSDo38Iux5S93AlSZIkqZ5Miqto0FA47gro15bVlz8BVxwG91y6/uJbKxbD778Ilx0Cyx7JXot+cMylsNfxjY9bkiRJkgoWKaWyY6i7iJg5fvz48TNnziw7lOYy9wb4xamwennttegP2+8FK5fB84+v//62wXDU92DcsY2NU5IkSZJeX/TkQ44UV9luh8EnZ8C242qvpbWwcPaGCfHOB8Gn7zQhliRJktRS2soOQCXbagycfCPc9i2Y83tY/EDtWNsg2GFvmPgJ2PP47H5kSZIkSWohpSfFEbErcAxwGLArsC3wHHAXMDWlNKPE8Kph4BCY8uVsW/ksLLoPBg2Dbff0cUuSJEmSWlrpSTHwNeDDwEPAdcCzwO7AB4APRMQZKaWLS4yvWoaMgDFTyo5CkiRJkhqiGZLi64FvpJRmd3wxIg4AbgS+GRHXpJQWlRKdJEmSJKlllb7QVkrpys4Jcf76n4CbgYHAfo2OS5IkSZLU+pphpPi1rMn3r27MmyOiu2cujS0mHEmSJElSKyl9pLg7EfFm4GBgJXBLyeFIkiRJklpQU44UR8RmwNXAZsDZKaXnNuZzKaUJ3bQ3ExhfXISSJEmSpFZQyEhxRCyIiLQJ27TXaKs/8GNgf+CnwH8UEaMkSZIkSZ0VNVI8D3h5E96/sKsX84R4GnA88DPgYyml1PvwJEmSJEnaUCFJcUrp4N62ERFtwE/IEuKfACemlNb2tl1JkiRJkrrTFPcUR8RAspHhDwJXASellNaVG5UkSZIkqdWVvvp0vqjWr8gS4ssxIZYkSZIkNUgzjBRfAhwOLAWeAs6NiM7vuTmldHOD45IkSZIktbhmSIp3yvdbA+e+xvturn8okiRJkqQqKT0pTikdWHYMkiRJkqRqKv2eYkmSJEmSymJSLEmSJEmqLJNiSZIkSVJlRUqp7BjqLiKWDR48eMQee+xRdiiSJEmSpDqYNWvWT1JKH93Uz1UlKf4bMBRYUMfTjM33D9fxHFJH9jmVwX6nMtjv1Gj2OZXBftd7D5sUlygiZgKklCaUHYuqwT6nMtjvVAb7nRrNPqcy2O/K4z3FkiRJkqTKMimWJEmSJFWWSbEkSZIkqbJMiiVJkiRJlWVSLEmSJEmqLFefliRJkiRVliPFkiRJkqTKMimWJEmSJFWWSbEkSZIkqbJMiiVJkiRJlWVSLEmSJEmqLJNiSZIkSVJlmRRLkiRJkirLpLgbETEqIq6IiIURsToiFkTE1IgYXkY7qobe9peI2CoiTomIX0XEoxGxKiKWR8RtEXFyRPhvXuupx29URJwQESnfTikyXrWGIvtdRLwrIn4REYvythZFxPSIOLwesavvKvD/du/P+9iT+XV2fkRcExHvqFfs6nsi4riI+E5E3BoRL+TXxGk9bMt8os4ipVR2DE0nIsYAdwDbANcCDwOTgIOAOcD+KaVljWpH1VBEf4mI04AfAIuAGcDjwLbAMcAw4BfA8cl/+KI+v1ERsSNwP9AfeANwakrpsiLjVt9WZL+LiC8DXwOWAr8l++3bGtgbmJFSOrvwL6A+qcD/230DOBtYBvyarO/tAnwAaANOTCn1KPFRa4mI+4C3AS8CTwJjgatTSh/bxHbMJxohpeTWaQNuABJweqfXv5W/fkkj23GrxlZEfwGmAEcC/Tq9vh1ZgpyAY8v+rm7NsRX9GwUEcBMwD/hm3sYpZX9Pt+baCrzGHp+//0Zgiy6ODyj7u7o1z1bQNXY7YC3wNLBNp2MH5e3ML/u7ujXHlveJXfNr44F5/5jWg3bMJxqwOVLcSUTsTPYfugXAmJTSug7HtiD7K3SQ/Ri+VO92VA2N6C8R8SXg68B3U0qn9zpo9Wn16HMRcQZwEdnFfwpwHo4Uq4MCr7H9gEfJZsKMTiktqWfc6tsK7HeTgbuA36SUPtjF8RfIZmFuUew3UF8XEQeSzeDbpJFi84nG8f7CDU3J99M7djyAlNIK4HZgCLBvg9pRNTSiv6zJ96/2og21jkL7XETsAVwAfDuldEuRgaqlFNXv9gN2Aq4Dnsvv8TwnIs7wvk51oah+9wjwCjApIrbueCAi3g1sQTZbRiqK+USDmBRvaPd8P7eb44/k+90a1I6qoa79JSLagBPz6vU9aUMtp7A+l/evH5NN0f9S70NTCyuq3+2T7xcDs8juJ74AmArcERF/iog39iJOtZZC+l1K6VngHLIZCg9FxA8j4vyI+BkwnWwq/6cKiFdqZz7RIG1lB9CEhuX75d0cb399ywa1o2qod3+5ABgHXJdSuqGHbai1FNnnziVb2OidKaVVvYxLra2ofrdNvj8N+BtwCHA38GbgQuAw4BqyqfxSYb93KaWpEbEAuAI4tcOhR4ErU0rP9DBGqSvmEw3iSPGmi3zf25uxi2pH1dDj/hIRnwXOIlut8IQig1JL26g+FxGTyEaHL0wp3Vn3qNTqNva3rn+H9x+XUvpDSunFlNKDwNFkK70e4FRqbaSNvsZGxNnAz4ErgTHA5sAEYD5wdUT8e51ilLpiPlEQk+INtf/FZVg3x4d2el+921E11KW/RMRngG8DDwEH5VO/JCigz3WYNj0X+EpxoamFFfVb91y+n59S+kvHA/lshfYZMZM2OUK1okL6Xb5Y0jfIFtr6fEppfkppZUppFtkfY54CzsoXR5KKYD7RICbFG5qT77ubm79rvu9ubn/R7agaCu8vEXEm8F3gAbKE+OkeR6dWVESfe0P++T2AlyMitW9kK08DXJq/NrW3AaslFH2Nfb6b4+1J8+CNC0strqh+d0S+n9H5QEppJXAP2f+t997UAKVumE80iPcUb6j9h+7QiOjXxdLn+wOryJbkb0Q7qoZC+0tEnEN2H/F9wHtSSkuLDVctoIg+txq4vJtj48n+Y3gb2UXdqdWC4n7rbiFbSX/XiBiYUnql0/Fx+X5B70NWCyiq322W77tbxK399c79Ueop84kGcaS4k5TSPLIVBEcDn+l0+Ktk945c1f4ssIgYEBFjI2JMb9pRtRXV7/JjXyFLiGcCB5sQqytF9LmU0qqU0ildbcBv8rf9KH/tp3X/Ump6BV5jlwI/JZtSeG7HYxHxHrKFtpbjavui0Gvsrfn+kxExsuOBiHgfWYLyMnBHsd9Arc58onyRkvdld5Z3yDvIVre8FvgrMBk4iGx6wn4ppWX5e0eTrXz5WEppdE/bkYrodxHxcbLFP9YC36Hre0wWpJSurNPXUB9S1G9dN23/M9kU6lNTSpfVIXz1UQVeY7che0bnLmTJyj1kq08fTbbozN+nlK6p/zdSX1DQNbYf2f3qhwArgF8BT5PdQnIE2aJHZ6aUvt2QL6WmFhFHAUfl1e3I/lg3n9ofV5amlL6Qv3c05hOlcvp0F1JK8yJiIvAvwHuBw4FFwMXAVzd2saKi2lE1FNRfdsr3/YEzu3nPn8gSZ1Wcv1EqQ4HX2GciYjLwZbJEeF+yROV3wPkpJacT6v8V0e9SSusi4nCyEbuPkPW7IcCzwHXAxSml6XX6Cup73g58vNNrO+cbwGPAF16vEa/VjeFIsSRJkiSpsrynWJIkSZJUWSbFkiRJkqTKMimWJEmSJFWWSbEkSZIkqbJMiiVJkiRJlWVSLEmSJEmqLJNiSZIkSVJlmRRLkiRJkirLpFiSJEmSVFkmxZIkSZKkyjIpliRJkiRVlkmxJEmSJKmyTIolSZIkSZVlUixJkiRJqiyTYkmSJElSZZkUS5IkSZIqy6RYkiRJklRZ/wf9kC69UJB1jQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 265,
       "width": 482
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_test = 300\n",
    "x_test = np.linspace(0.02, 1.05, N_test)\n",
    "Phi_test = np.stack([x_test ** m for m in range(M)], axis=-1)\n",
    "\n",
    "t_map = np.ravel(Phi_test @ w_map)\n",
    "t_ml = np.ravel(Phi_test @ w_ml)\n",
    "plt.plot(x_test, t_map, label=\"ML\", c=\"tab:green\")\n",
    "plt.plot(x_test, t_ml, label=\"MAP\", c=\"tab:orange\")\n",
    "plt.scatter(x, t, c=\"tab:blue\")\n",
    "plt.title(\"Estimation comparisson\", fontsize=15)\n",
    "plt.legend(fontsize=13);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ${\\bf w}_\\text{MAP}$ for different $\\alpha$ values\n",
    "\n",
    "The larger $\\alpha$ is with respect to the true $\\alpha$, the more we overfit the data; the smaller $\\alpha$ with respect to the true $\\alpha$, the more the estimation tends to zero (resp. it implies that our prior beliefs about the true weigths of the model are that they are close to zero with much certainty)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 266,
       "width": 474
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "α_low = 0.0001\n",
    "α_high = 100.5\n",
    "\n",
    "w_map = inv(α * np.eye(M) + Phi.T @ Phi) @ Phi.T @ t[:, None]\n",
    "w_map_high = inv(α_high * np.eye(M) + Phi.T @ Phi) @ Phi.T @ t[:, None]\n",
    "w_map_low = inv(α_low * np.eye(M) + Phi.T @ Phi) @ Phi.T @ t[:, None]\n",
    "w_list = [w_map_high, w_map, w_map_low]\n",
    "labels = [\"high\", \"true\", \"low\"]\n",
    "for w, label in zip(w_list, labels):\n",
    "    t_map = np.ravel(Phi_test @ w)\n",
    "    plt.plot(x_test, t_map, label=label)\n",
    "    plt.scatter(x, t, c=\"tab:red\")\n",
    "plt.legend(fontsize=13)\n",
    "plt.title(r\"MAP estimations for varying $\\alpha$\", fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How many datapoints to make ${\\bf w}_{ML}$ well defined?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed(31415)\n",
    "N, M = 11, 11\n",
    "α = 1.3\n",
    "x = np.linspace(0, 1, N) + np.random.rand(N) * 0.05\n",
    "t = 3 * x + 1.2 + np.random.randn(N) / α\n",
    "Phi = np.stack([x ** m for m in range(M)], axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2274075348029745e-55"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.det(Phi.T @ Phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.matrix_rank(Phi.T @ Phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([29.05262,  6.91538,  0.80405,  0.06404,  0.00329,  0.00012,\n",
       "        0.     ,  0.     ,  0.     ,  0.     ,  0.     ])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eigvals(Phi.T @ Phi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[      15.82421],\n",
       "       [    -748.33972],\n",
       "       [   11341.91667],\n",
       "       [  -79628.01709],\n",
       "       [  313876.25215],\n",
       "       [ -754581.09779],\n",
       "       [ 1135828.10449],\n",
       "       [-1053178.02315],\n",
       "       [  561536.39252],\n",
       "       [ -143877.66896],\n",
       "       [    9425.1283 ]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_ml = inv(Phi.T @ Phi) @ Phi.T @ t[:, None]\n",
    "w_ml"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
